Chapter 11.2, Problem 40WE

To determine

To Construct: An isosceles triangle whose area is equal to the area of scalene triangle.

Explanation of Solution

Given: Scalene triangle.

Let the area of the scalene triangle is $32c{m}^2$

Now

We have to draw the isosceles triangle

i.e.

Two of its sides area equal.

Let $OC$ be the altitude and $AB$ is the base.

Here

  $\begin{array}{l}A0=OB\\ A=\frac{1}{2}bh\\ 32=\frac{1}{2}bh\\ bh=64\end{array}$

Taking

  $\begin{array}{l}b=4\\ h=16\end{array}$

i.e.

  $\begin{array}{l}AB=4cm\\ OC=16cm\end{array}$

Thus the isosceles triangle shown below.