Question

The sides of the pentagon are consecutive even integers. Find the length of the shortest side if the second longest side is 24% of the perimeter.

Answer 1

6 units

Explanation:

There are 5 sides in a pentagon. If the shortest side is x, then the other 4 sides are x+2, x+4, x+6, and x+8.

The perimeter is therefore:

P = x + x+2 + x+4 + x+6 + x+8

P = 5x + 20

The second longest side (x+6) is 24% of the perimeter.

x + 6 = 0.24 (5x + 20)

x + 6 = 1.2x + 4.8

1.2 = 0.2 x

x = 6

The length of the shortest side is 6 units.