Chapter 8, Problem 6CR

To determine

To calculate: the length of diagonal of a rectangle

Answer to Problem 6CR

The length of diagonal is $2\sqrt{41}$

Explanation of Solution

Given Information: The sides of a rectangle are 10 and 8 units.

Formula used:

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

Calculation: Consider the rectangle given below.

  

The length of the sides is given as a=10, b=8. So, the length of the diagonal can be calculated using the above formula as,

  $\begin{array}{c}d=\sqrt{{10}^2+8^2}\\ =\sqrt{164}\\ =2\sqrt{41}\\ =12.8\end{array}$