Chapter 11.6, Problem 1P

To determine

To find: the length of the diagonal of the given rectangle.

Answer to Problem 1P

  $AD=65cm$ .

Explanation of Solution

Given:

The dimensions of given rectangle are $33\text{cm}\text{by}56\text{cm}$ .

And the rectangle is shown below:

  

Calculation:

As the dimensions of given rectangle are $33\text{cm}\text{by}56\text{cm}$ .

From right triangle ABD, of the diagonal AD, in the rectangle ABCD.

By using Pythagoras theorem, $A{D}^2=A{B}^2+B{D}^2$

Thus,

  $\begin{array}{l}A{D}^2=A{B}^2+B{D}^2\\ ={33}^2+{56}^2\left\{\text{substitutes the given value}\right\}\\ =1089+3136\{\because {33}^2=1089,{56}^2=3136\}\\ =4225\left\{\text{add the both terms}\right\}\end{array}$

  $\begin{array}{l}\therefore AD=\sqrt{4225}\left\{\text{taking square root on both the sides}\right\}\\ \Rightarrow AD=\sqrt{{65}^2}\{\text{simplify}}\\ AD=65\{\sqrt{a^2}=a\}\end{array}$

Hence, the length of the diagonal of the given rectangle is $AD=65cm$ .