Question

A heptagon has a perimeter of 132 feet. Four of the sides are the same length and the remaining sides are half as long how long are the short sides?

Answer 1

A heptagon is a 7-sided polygon.

Let x = length of the longer sides, thus

x/2 = length of the shorter sides.

We know 4 of the sides are longer and 3 are shorter, and the perimeter is 132 feet, thus:

$x+x+x+x+\frac{x}{2}+\frac{x}{2}+\frac{x}{2}=132$

Simplifying:

$\begin{gathered} 4x+\frac{3x}{2}=132 \\ \frac{11x}{2}=132 \\ 11x=264 \\ x=\frac{264}{11}=24 \end{gathered}$

The shorter sides measure 24/2 = 12 feet

Answer:

The shorter sides are 12 feet.