Question

describe how the given changes to the dimensions of the figure will affect its perimeter or area. what happens to the perimeter of a regular hexagon with side lengths of 5 units when each side length is increased by a factor of 4? > move an answer into each space provided. the perimeter of the resulting triangle will be increased by 4 by 16 by a factor of 4 by a factor of 16

Explanation:

Step1: Find original perimeter

A regular hexagon has 6 equal - side lengths. If the original side length $s = 5$ units, the original perimeter $P_1=6s$. So $P_1 = 6\times5=30$ units.

Step2: Find new side length

Each side length is increased by a factor of 4. The new side length $s_2 = 4s$. Since $s = 5$ units, $s_2=4\times5 = 20$ units.

Step3: Find new perimeter

The new perimeter $P_2=6s_2$. Substitute $s_2 = 20$ into the formula, we get $P_2=6\times20 = 120$ units.

Step4: Find the ratio of perimeters

Calculate $\frac{P_2}{P_1}=\frac{120}{30}=4$. This means the perimeter is increased by a factor of 4.

Answer:

by a factor of 4