Question

on the grid in problem 1 measures 5 ft by 5 ft. use the length of c the original and scaled figures to complete the table. le length (ft) 5 10 15 20 e length (ft) 1 2 3 4 × ed by a factor of 4. apply this scale factor to complete the table. length (ft) 6 2 × 4 2313

Explanation:

First Table (Original to Scaled, Scale Factor Calculation)

We know that the grid square is 5 ft by 5 ft. Let's assume the first row is the original length (let's call it \( O \)) and the second row is the scaled length (let's call it \( S \)).

Looking at the first column: \( O = 5 \) ft, \( S = 1 \) ft? Wait, no, maybe the original is the grid square (5 ft) and the scaled is the number of grid squares? Wait, maybe the first row is the length in grid units (each grid is 5 ft), and the second row is the actual length? Wait, no, the problem says "the grid in Problem 1 measures 5 ft by 5 ft". Let's re-express.

Wait, the first table: first row is "length (ft)" with 5, 10, 15, 20. Second row is "length (ft)" with 1, 2, 3, 4? Wait, no, maybe the first row is the length in terms of grid squares (each grid square is 5 ft), and the second row is the number of grid squares? Wait, no, let's check the scale factor.

If original length (ft) is 5, scaled length (ft) is 1? No, that would be a scale factor of \( \frac{1}{5} \). But looking at the numbers: 5, 10, 15, 20 (original) and 1, 2, 3, 4 (scaled). So the scale factor is \( \frac{\text{scaled length}}{\text{original length}} = \frac{1}{5} \)? Wait, no, 5 ft original corresponds to 1 ft scaled? Wait, maybe the original is the length in grid squares (each grid square is 5 ft), so 1 grid square is 5 ft, 2 grid squares is 10 ft, etc. Then the scaled length (maybe in grid squares) is 1, 2, 3, 4. Wait, the problem says "use the length of the original and scaled figures to complete the table". Maybe the first row is the length of the original figure (in ft), and the second row is the length of the scaled figure (in ft), and we need to find the scale factor.

Looking at the first column: original length = 5 ft, scaled length = 1 ft? No, that seems odd. Wait, maybe the first row is the length in terms of the number of grid squares (each grid square is 5 ft), so 1 grid square is 5 ft, 2 grid squares is 10 ft, 3 is 15 ft, 4 is 20 ft. Then the scaled length (in grid squares) is 1, 2, 3, 4. So the scale factor from original (grid squares) to scaled (grid squares) is 1? No, that doesn't make sense. Wait, maybe the original figure has a length of 5 ft (1 grid square), and the scaled figure has a length of 1 ft? No, that would be a reduction. Wait, the numbers in the second row are 1, 2, 3, 4, and the first row is 5, 10, 15, 20. So 5 divided by 5 is 1, 10 divided by 5 is 2, 15 divided by 5 is 3, 20 divided by 5 is 4. Ah! So the scale factor is \( \frac{1}{5} \), because scaled length = original length \( \times \frac{1}{5} \). Let's verify:

• For original length 5 ft: \( 5 \times \frac{1}{5} = 1 \) ft (matches the first entry in the second row)
• For original length 10 ft: \( 10 \times \frac{1}{5} = 2 \) ft (matches the second entry)
• For original length 15 ft: \( 15 \times \frac{1}{5} = 3 \) ft (matches the third entry)
• For original length 20 ft: \( 20 \times \frac{1}{5} = 4 \) ft (so the fourth entry in the second row is 4)

So the scale factor is \( \frac{1}{5} \), and the fourth entry in the second row is 4.

Second Table (Scaled by a Factor of 4)

The problem says "scaled by a factor of 4". So scaled length = original length \( \times 4 \). The first row is "length (ft)" with 6, 2, and two blanks. Wait, maybe the first row is the original length, and the second row (not shown fully) is the scaled length? Wait, the table has "length (ft)" with 6, 2, and two empty cells, and an arrow with \( \times 4 \). So we need to compute scaled length for the empty cells? Wait, maybe the first row is original length, and we need to find scaled length by multiplying by 4. But the problem says "apply this scale factor to complete the table". Wait, maybe the first row is the original length, and we need to find the scaled length (original \( \times 4 \)). But the given original lengths are 6 and 2, and we need to fill the next two? Wait, maybe the table is:

Original Length (ft)	6	2	?	?

Wait, no, the arrow is \( \times 4 \), so scaled length = original length \( \times 4 \). Wait, maybe the first row is the scaled length? No, the arrow is from the first row to the second row with \( \times 4 \), so second row = first row \( \times 4 \)? Wait, no, the arrow direction: the first row is on the left, and the arrow is \( \times 4 \) going to the right? Wait, the image shows:

"length (ft)" | 6 | 2 | |
--- | --- | --- | --- | ---

\( \times 4 \)

Wait, maybe the first row is the original length, and we need to find the scaled length by multiplying by 4. But the problem says "scaled by a factor of 4", so scaled length = original length \( \times 4 \). Wait, but the first entry in the first row is 6, so scaled length is \( 6 \times 4 = 24 \), second entry is 2, so scaled length is \( 2 \times 4 = 8 \). But the table has two empty cells in the first row? Wait, maybe the first row is the scaled length, and the original length is scaled length \( \div 4 \)? No, the problem says "scaled by a factor of 4", so if the original length is \( L \), scaled length is \( 4L \).

Wait, maybe the table is:

Original Length (ft)	6	2	a	b

But the problem says "complete the table", so maybe the first row is original length, and we need to fill the scaled length. But the given first row has 6, 2, and two blanks. Wait, maybe the first row is the scaled length, and we need to find the original length? No, the scale factor is 4, so original = scaled \( \div 4 \). But the problem says "scaled by a factor of 4", so scaled = original \( \times 4 \).

Assuming the first row is original length, and we need to find scaled length (original \( \times 4 \)):

• For original length 6 ft: scaled length = \( 6 \times 4 = 24 \) ft
• For original length 2 ft: scaled length = \( 2 \times 4 = 8 \) ft

But the table has two empty cells in the first row. Maybe the first row is the number of grid squares, and each grid square is 5 ft? No, the problem says "the grid in Problem 1 measures 5 ft by 5 ft", so maybe the first table is about scaling with a scale factor of \( \frac{1}{5} \) (since 5 ft original becomes 1 ft scaled), and the second table is scaling by 4.

Wait, let's re-express the first table:

First table:

Original Length (ft)	5	10	15	20

So the pattern is Scaled Length = Original Length \( \div 5 \), because \( 5 \div 5 = 1 \), \( 10 \div 5 = 2 \), \( 15 \div 5 = 3 \), \( 20 \div 5 = 4 \). So the scale factor is \( \frac{1}{5} \)…

Answer:

The problem says "scaled by a factor of 4". So scaled length = original length \( \times 4 \). The first row is "length (ft)" with 6, 2, and two blanks. Wait, maybe the first row is the original length, and the second row (not shown fully) is the scaled length? Wait, the table has "length (ft)" with 6, 2, and two empty cells, and an arrow with \( \times 4 \). So we need to compute scaled length for the empty cells? Wait, maybe the first row is original length, and we need to find scaled length by multiplying by 4. But the problem says "apply this scale factor to complete the table". Wait, maybe the first row is the original length, and we need to find the scaled length (original \( \times 4 \)). But the given original lengths are 6 and 2, and we need to fill the next two? Wait, maybe the table is:

Original Length (ft)	6	2	?	?

Wait, no, the arrow is \( \times 4 \), so scaled length = original length \( \times 4 \). Wait, maybe the first row is the scaled length? No, the arrow is from the first row to the second row with \( \times 4 \), so second row = first row \( \times 4 \)? Wait, no, the arrow direction: the first row is on the left, and the arrow is \( \times 4 \) going to the right? Wait, the image shows:

"length (ft)" | 6 | 2 | |
--- | --- | --- | --- | ---

\( \times 4 \)

Wait, maybe the first row is the original length, and we need to find the scaled length by multiplying by 4. But the problem says "scaled by a factor of 4", so scaled length = original length \( \times 4 \). Wait, but the first entry in the first row is 6, so scaled length is \( 6 \times 4 = 24 \), second entry is 2, so scaled length is \( 2 \times 4 = 8 \). But the table has two empty cells in the first row? Wait, maybe the first row is the scaled length, and the original length is scaled length \( \div 4 \)? No, the problem says "scaled by a factor of 4", so if the original length is \( L \), scaled length is \( 4L \).

Wait, maybe the table is:

Original Length (ft)	6	2	a	b

But the problem says "complete the table", so maybe the first row is original length, and we need to fill the scaled length. But the given first row has 6, 2, and two blanks. Wait, maybe the first row is the scaled length, and we need to find the original length? No, the scale factor is 4, so original = scaled \( \div 4 \). But the problem says "scaled by a factor of 4", so scaled = original \( \times 4 \).

Assuming the first row is original length, and we need to find scaled length (original \( \times 4 \)):

• For original length 6 ft: scaled length = \( 6 \times 4 = 24 \) ft
• For original length 2 ft: scaled length = \( 2 \times 4 = 8 \) ft

But the table has two empty cells in the first row. Maybe the first row is the number of grid squares, and each grid square is 5 ft? No, the problem says "the grid in Problem 1 measures 5 ft by 5 ft", so maybe the first table is about scaling with a scale factor of \( \frac{1}{5} \) (since 5 ft original becomes 1 ft scaled), and the second table is scaling by 4.

Wait, let's re-express the first table:

First table:

Original Length (ft)	5	10	15	20

So the pattern is Scaled Length = Original Length \( \div 5 \), because \( 5 \div 5 = 1 \), \( 10 \div 5 = 2 \), \( 15 \div 5 = 3 \), \( 20 \div 5 = 4 \). So the scale factor is \( \frac{1}{5} \) (scaled = original \( \times \frac{1}{5} \)).

Second table:

The problem says "scaled by a factor of 4". So Scaled Length = Original Length \( \times 4 \). The table has:

Original Length (ft)	6	2	?	?

Wait, maybe the first row is the scaled length, and we need to find the original length? No, the scale factor is 4, so original = scaled \( \div 4 \). But the problem says "scaled by a factor of 4", so scaled = original \( \times 4 \).

Alternatively, maybe the first row is the length in grid squares (each grid square is 5 ft), and we need to find the actual length. But the first table already used 5 ft per grid square.

Wait, maybe the second table is:

Length (ft)	6	2	a	b

But the problem says "complete the table", so maybe the first row is the original length, and we need to fill the scaled length. So for the first two entries:

• 6 ft original: scaled length = \( 6 \times 4 = 24 \) ft
• 2 ft original: scaled length = \( 2 \times 4 = 8 \) ft

But the table has two empty cells in the first row. Maybe the first row is the number of grid squares, and each grid square is 5 ft, but that doesn't fit with 6 and 2.

Alternatively, maybe the second table is:

Original Length (ft)	6	2	c	d

But without more information, we can only solve the first table's fourth entry and the second table's first two scaled entries.

First Table Completion:

Step 1: Identify the pattern

Original length (ft): 5, 10, 15, 20
Scaled length (ft): 1, 2, 3,?

We see that Scaled Length = Original Length \( \div 5 \) (since \( 5 \div 5 = 1 \), \( 10 \div 5 = 2 \), \( 15 \div 5 = 3 \)).

Step 2: Calculate the fourth scaled length

For original length 20 ft:
Scaled length = \( 20 \div 5 = 4 \) ft.

Second Table Completion (assuming original length to scaled length, scale factor 4):

Step 1: Scale the first original length

Original length = 6 ft
Scaled length = \( 6 \times 4 = 24 \) ft.

Step 2: Scale the second original length

Original length = 2 ft
Scaled length = \( 2 \times 4 = 8 \) ft.

Final Answers for the Tables:

• First table (scaled length for 20 ft original): \( \boldsymbol{4} \)
• Second table (scaled lengths for 6 ft and 2 ft original): \( \boldsymbol{24} \) and \( \boldsymbol{8} \) (assuming the table has two more original lengths, but with given data, we can only compute these)

(Note: The problem's table might have missing context, but based on the given numbers, the first table's fourth scaled length is 4, and the second table's scaled lengths for 6 and 2 are 24 and 8 respectively.)