Chapter 10.1, Problem 33P

The area of a square is 625 cm². What is the measure of the diagonal to the nearest tenth?

To determine

To find the measure of the diagonal of the square to the nearest tenth.

Answer to Problem 33P

The diagonal of the square is $35.4cm$ .

Explanation of Solution

Given information:

The area of the square is $625c{m}^2$ .

Formula used:

The following formula is used:

  $\begin{array}{l}{\left(hypotenuse\right)}^2={\left(base\right)}^2+{\left(height\right)}^2\\ \text{Side of a square}=\sqrt{\text{Area}}\end{array}$

Calculation:

Calculate the side of the square:

  $\begin{array}{l}\text{Side of a square}=\sqrt{\text{Area}}\\ \text{Side of a square}=\sqrt{\text{625}c{m}^2}\\ \text{Side of a square}=25cm\end{array}$

Calculate the diagonal of the square.

  $\begin{array}{l}{\left(hypotenuse\right)}^2={\left(base\right)}^2+{\left(height\right)}^2\\ {\left(hypotenuse\right)}^2={\left(25\right)}^2+{\left(25\right)}^2\\ hypotenuse=\sqrt{625+625}\\ hypotenuse=\sqrt{1250}\\ hypotenuse=35.4\end{array}$

Hence, the diagonal of the square is $35.4cm$ .