Question

A pair of adjacent sides of a rectangle are in ratio 3:4if its diagonal is 20cm find the lengths of the sides and the perimeter of the rectangle​

Answer 1

Answer:

12 cm and 16 cm; 56 cm

Step-by-step explanation:

As the adjacent sides of the rectangle are in the ratio 3:4,

we can assign them as 3x and 4x.

Along with the diagonal, these adjacent sides form a right triangle with the diagonal as the hypotenuse.

Given: diagonal = 20 cm

=> Hypotenuse = 20 cm

Using Pythagorean theorem, we get:

(3x)² + (4x)² = (20)²

=> 9x² + 16x² = 400

=> 25x² = 400

=> x² = 16

=> x = +4 or x = -4

As "x" relates to length, x = -4 is inadmissible

=> x = 4

The required sides are 3x and 4x

=> The adjacent sides are 12 cm and 16 cm

Perimeter of rectangle = 2*(sum of adjacent sides)

                                      = 2*(12 + 16) cm

                                      = 2*28 cm

                                      = 56 cm