Chapter 14.5, Problem 24PSC

To determine

To construct a square that has area twice from the given area of square.

Explanation of Solution

Given:

The given area of square.

Calculation:

The square that has area twice from the given area of squarecan be constructed as follows-

Let the side of the given square be $a$ unit.

So the area of the square will be $a^2$

Now, the area of new square whose side is $b$ unit.

Therefore the area will be equal when

  $\begin{array}{l}{b}^2=2a^2\\ b=\sqrt{2}a\end{array}$

Step 1- Draw the square of side $a$ unit.

Step 2- Draw another square of side $\sqrt{2}a$ unit.