Question

Adjacent sides of a rectangle are in the ratio 5 : 12, if the perimeter of the rectangle is 34 cm, find the length of the diagonal.​

Answer 1

Given,

Ratio of the adjacent sides of the rectangle = 5 : 12

• Let 5x and 12x be the two adjacent sides.

We know that the sum of all sides of a rectangle is equal to its perimeter.

Thus,

$\sf{5x + 12x + 5x + 12x = 34\:cm\:(given)}$

$\sf{→34x = 34}$

$\sf\large{→x =\frac{ 34}{34}}$

$\sf\large{→x = 1\:cm}$

Therefore, the adjacent sides are 5 cm and 12 cm respectively.

i.e. l = 12 cm, b = 5 cm

Length of the diagonal $\sf{= \sqrt{({l}^{2} + {b}^{2})}}$

$\sf= \sqrt{(122 + 52)}$

$\sf= \sqrt{(144 + 25)}$

$\sf{= \sqrt{169}}$

$\sf{= 13\:cm}$

Hence, the length of the diagonal is 13 cm.