Chapter 14.6, Problem 17PSC

To determine

To construct an isosceles righttriangle equal in area to a given triangle.

Explanation of Solution

Given:

The given triangle.

Calculation:

The right isosceles triangle equal in area to a given triangle can be constructed as follows-

Step 1- Let the area of the given triangle be A.

Step 2- Let the length of the equal sides of right isosceles triangle be $b$ .

Step 3- Now, construct the right angled isosceles triangle in such a way such that

  $\begin{array}{l}\frac{1}{2}\times b^2=A\\ \Rightarrow b=\sqrt{2A}\end{array}$

Step 4- now, draw the isosceles triangle whose two sides are equal to the length $\sqrt{2A}$

Step 5- Join all the vertices to get the required right isosceles triangle.