Chapter 8, Problem 7CR

To determine

To calculate: the length of the side of a square

Answer to Problem 7CR

The length of a side is $7\sqrt{2}$

Explanation of Solution

Given Information: The diagonal of a square has length 14.

Formula used:

The relationship between the length of a side of square a and its diagonal d is obtained by using Pythagoras theorem. The square has all of its angles as right angle. Hence, the diagonal acts as hypotenuse, which can be expressed in terms of length of the side a$\begin{array}{l}{d}^2=a^2+a^2\\ d=\sqrt{2}a\end{array}$

Calculation: Consider the square given below.

  

The length of the diagonal is given as 14. So, the length of the side can be calculated using the above formula as ,

  $\begin{array}{c}a=\frac{d}{\sqrt{2}}\\ =\frac{14}{\sqrt{2}}\\ =7\sqrt{2}\end{array}$