An irregular pentagon is a five sided figure. The two longest sides of a pentagon are each three tim

[math_celebrity]

An irregular pentagon is a five sided figure. The two longest sides of a pentagon are each three times as long as the shortest side. The remaining two sides are each 8m longer than the shortest side. The perimeter of the Pentagon is 79m. Find the length of each side of the Pentagon.

Let long sides be l. Let short sides be s. Let medium sides be m. We have 3 equations:

1. 2l + 2m + s = 79
2. m = s + 8
3. l = 3s

Substitute (2) and (3) into (1):
2(3s) + 2(s + 8) + s = 79

Multiply through and simplify:
6s + 2s + 16 + s = 79
9s + 16 = 79

Using our equation calculator, we get s = 7.
This means from Equation (2):
m = 7 + 8
m = 15

And from equation (3):
l = 3(7)
l = 21