Chapter 9, Problem 9CUR

To determine

To Find: the side of a square.

Answer to Problem 9CUR

The side of the square is, $AB=2\sqrt{2}$ units.

Explanation of Solution

Given information: ABCE is a square; $AC=4\text{ units}$ .

Since the diagonal of a square is of $4$ units,

We know that the diagonal of a square and its sides makes a right − angled triangle.

So, let the side of the given square ABCE be $x$ ,

  $\begin{array}{l}{x}^2+x^2=4^2,\\ \Rightarrow 2x^2=16,\\ \Rightarrow x^2=8,\\ \Rightarrow x=\pm 2\sqrt{2}.\end{array}$

Since, the length of the side of a square cannot be negative, the value of $AB$ is $2\sqrt{2}$ units, that is, $AB=2\sqrt{2}\text{ units}$.