Question

Find the length of each side of the polygon for the given perimeter.

Answer 1

As the picture highlights, the opposite sides have the same lengths. The perimeter is the sum of all lengths, so we have

$P = 2(2s-5) + 2(4s-13)$

Plug the required value for the perimeter and expand the right hand side:

$108 = 4s-10 + 8s-26$

Simplify the right hand side:

$108 = 12s-36$

Add 36 to both sides:

$144 = 12s$

Divide both sides by 12:

$12 = s$

Now that we know the value for s, let's deduce the lengths of the sides:

$2s-5 = 2\cdot 12 - 5 = 24-5 = 19$

$4s-13 = 4\cdot 12 - 13 = 48-13 = 35$