The two unequal sides of a rectangle are in the ratio of 3 : 4. If the perimeter is 42 cm, then the length of diagonal will be:

Correct option is C

Given:

The two unequal sides of a rectangle are in the ratio of 3: 4.

The perimeter = 42 cm

Formula used:

Perimeter of Rectangle = 2(l + b)

Diagonal of Rectangle = √(l²+ b²)

Solution:

Let the length of unequal sides of the rectangle be = 3x and 4x.

Perimeter of Rectangle = 42 cm

=> 2(3x + 4x) = 42

=> 14x = 42

=> x = 3

Length of unequal sides = 9 cm and 12 cm

Now Diagonal of Rectangle

​$$\begin{aligned}&\implies \sqrt{(9)^2 + (12)^2} \\&\implies \sqrt{81 + 144} \\&\implies D = \sqrt{225} = 15 \, \text{cm}\end{aligned}$$​   

Hence, option (c) is correct answer.