Question

The trim around the three edges of an isosceles triangular roofline measures 137 feet. The base of the triangle is 3 feet less than two times the length of its legs. What is the length of the triangle's base?

Answer 1

Let's begin by identifying key information given to us:

The trim around the triangle = 137 feet

base is 3 feet less than two times the length of its legs

`\begin{gathered} b=2a-3 \\ Let\colon a=\text{ the length of the leg of the triangle} \end{gathered}`

We will solve this by equating the perimeter of the triangle with 137 feet. We have:

`\begin{gathered} Perimeter=2a+b \\ But,b=2a-3 \\ P=137 \\ 137=2a+2a-3 \\ \text{Add ''3'' to both sides, we have:} \\ 137+3=4a-3+3 \\ 140=4a \\ \text{Divide both sides by 4, we have:} \\ (140)/(4)=(4a)/(4) \\ a=35ft \\ \\ b=2a-3 \\ b=2(35)-3=70-3 \\ b=67ft \end{gathered}`