Question

4 identify the scale factor and its reciprocal for side lengths in the table. then, complete the tal
original side length (ft) \t7 \t3 \t9 \t
scaled side length (ft) \t35 \t\t\t50 \t× \t×
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Explanation:

Step1: Find the scale factor

To find the scale factor, we divide the scaled side length by the original side length. For the first pair, original is 7 ft and scaled is 35 ft. So scale factor $= \frac{35}{7} = 5$.

Step2: Find the reciprocal of the scale factor

The reciprocal of 5 is $\frac{1}{5}$.

Step3: Calculate the missing scaled side lengths

For original side length 3 ft: scaled length $= 3 \times 5 = 15$ ft.
For original side length 9 ft: scaled length $= 9 \times 5 = 45$ ft.

Step4: Calculate the missing original side length

For scaled side length 50 ft: original length $= 50 \times \frac{1}{5} = 10$ ft.

Answer:

Scale factor is 5, its reciprocal is $\frac{1}{5}$.
Filled table:

• Original side length (ft): 7, 3, 9, 10
• Scaled side length (ft): 35, 15, 45, 50