Question

A rectangle with diagonals of length 20cm has sides in the ratio 2 : 1. Find the :

a) Perimeter b) Area of the rectangle

help!!

Answer 1

Step-by-step explanation:

Given, length of each diagonal of a rectangle = 20cm

Given, ratio of its sides = 2 : 1

let the length of rectangle = 2x & breadth = x

Using Pythagoras theorem,

(2x) ^2 + (x) ^2 = (20)^2

=> 4x^2 + x^2 = 400 => 5x^2 = 400 => x^2 = 80

=> x = √80 = 4√5

=> length of rectangle = 8√5 & breadth = 4√5

.•. a) Perimeter = 2 ( l + b) = 2 ( 8√5 + 4√5 )

= 2 ( 12√5 ) = 24√5 cm

b) Area of the rectangle = l x b = 8√5 x 4√5

= 32(5) = 160 cm^2