Question

each square on the grid in problem 1 measures 5 ft by 5 ft. use the length of corresponding line segments on the original and scaled figures to complete the table.
original side length (ft) \t5 \t10 \t15 \t20
scaled side length (ft) \t1 \t2 \t3 \t4 \t× blank
3
a figure is scaled by a factor of 4. apply this scale factor to complete the table.
original side length (ft) \t6 \t2 \tblank \tblank \t× 4

Explanation:

For the first table (top one, assuming scale factor from original to scaled is $\frac{1}{5}$? Wait, no, the first table's original is 5,10,15,20 and scaled is 1,2,3,4. So scale factor is $\frac{\text{scaled}}{\text{original}}=\frac{1}{5}$? Wait, but the second problem is scale factor 4. Let's focus on the second problem (problem 3):

Step1: Understand scale factor

Scale factor is 4, so scaled length = original length × 4.

Step2: Calculate for original = 6

Scaled length = $6 \times 4 = 24$

Step3: Calculate for original = 2

Scaled length = $2 \times 4 = 8$

Step4: Let's assume we can choose original lengths, say 3 and 5 (any values, but let's pick simple ones)

For original = 3: Scaled = $3 \times 4 = 12$
For original = 5: Scaled = $5 \times 4 = 20$

Step1: Find scale factor

Scale factor $k = \frac{\text{scaled length}}{\text{original length}}$. For original=5, scaled=1: $k = \frac{1}{5}$.

Step2: Verify with other values

For original=10: $10 \times \frac{1}{5} = 2$ (matches). For original=15: $15 \times \frac{1}{5} = 3$ (matches). For original=20: $20 \times \frac{1}{5} = 4$ (matches).

Answer:

(for problem 3 table, filling scaled lengths and possible original lengths):

original side length (ft)	6	2	3	5

(Note: The original length columns can have any values, we chose 3 and 5 as examples. The key is multiplying by 4. For the first table, the scale factor is $\frac{1}{5}$ since $5 \times \frac{1}{5}=1$, $10 \times \frac{1}{5}=2$, etc. So first table's scale factor box is $\frac{1}{5}$.)

For the first table: