A vacant city lot is being turned in to a garden. the neighbors want to fence in a triangular section of the lot and plant flowers there. the longest side of the triangular sec is 8 feet shorter than twice the shortest side. the third side is 4 feet longer than the shortest side. the perimeter is 56 feet. how long is each side?

Hi there,

First of all, we see what are looking for.

We want to find the length of each side

What do we know?

Perimeter is 56

We are also given relation of between all the sides

But first we make some suggestions to the problem

Say that x is the shortest side

That means the longest is 2x-8

and the thirst side is x+4

Now we the desired information.

Perimeter=56=x+2x-8+x+4

we solve for x

combining like terms we get

4x-4=56

subtract 4 from both side

4x-4+4=56+4

4x=60

divide by 4 both side

4x/4=60/4

x=15

Shortest side is 15

longest side is 2 (15) - 8=30-8=22

3rd side is 15+4=19

if we add them up

15+22+19=56

Inside plus outside inside plus outside from middle to lenth out from first.