Question

1. the polygons are similar.

a) original perimeter = 66 ft. $k = \frac{3}{4}$
find the new perimeter.
b) new perimeter = 34 in. $k = \frac{5}{2}$
find the old perimeter.

Explanation:

Step1: Relate perimeters to scale factor

For similar polygons, $\text{New Perimeter} = k \times \text{Original Perimeter}$

Part a)

Step2: Substitute given values

$\text{New Perimeter} = \frac{3}{4} \times 66$

Step3: Calculate the product

$\text{New Perimeter} = \frac{198}{4} = 49.5$

Part b)

Step4: Rearrange formula for old perimeter

$\text{Old Perimeter} = \frac{\text{New Perimeter}}{k}$

Step5: Substitute given values

$\text{Old Perimeter} = \frac{34}{\frac{5}{2}}$

Step6: Simplify the division

$\text{Old Perimeter} = 34 \times \frac{2}{5} = \frac{68}{5} = 13.6$

Answer:

a) 49.5 ft
b) 13.6 in