Question

Adjacent sides of a rectangle are 9cm and 40cm. Find the length of its diagonal. ​

Answer 1

use Pythagoras theorem to find the diagonal of a rectangle.

Answer 2

Answer :-

• Length of the diagonal = 41cm.

Given :-

• Adjacent sides of a rectangle = 40cm,9cm.

To find :-

• Length of the diagonal.

Solution :-

We know that the adjacent angles of a rectangle are 9cm and 40cm.

We are asked to find the length of the diagonal.

Let AC be diagonal.

To find the diagonal of the rectangle we need to use the Formula given below :-

$\boxed{\sf {(Perpendicular)}^{2} + {(Base)}^{2} = {(Hypotenuse})^{2}}$

• Pythagoras theorem.

In ∆CBA, Using Pythagoras theorem,

$\implies \sf {(AB)}^{2} + {(BC)}^{2} ={( AC)}^{2}$

$\implies \sf {(40)}^{2} + {(9)}^{2} ={( AC)}^{2}$

$\implies \sf 1600 + 81={( AC)}^{2}$

$\implies \sf {( AC)}^{2} = 1681$

$\implies \sf AC = \sqrt{1681}$

$\implies \sf AC = 41cm$

Therefore, Length of the diagonal = 41cm.

[ NOTE :- SEE THE ATTACHMENT ]