The area of the kite is 48 cm2 What are the lengths of the d

The area of the kite is 48 cm^2. What are the lengths of the diagonals? PR = _____ QS = _____

Solution

The area of a kite is given by the formula

A = 1/2 (d1* d2 )

where d1 and d2 are the lengths of the kite\'s diagonals:

d1 = x + 2x = 3x

d2 = x +x = 2x

=> A = 1/2 ( 2x * 3x )

=> A = 0.5 * 6x^2

=> A = 3x^2

Given Are of the kite is 48 cm^2

=> 3x^2 = 48

=> x^2 = 48/3 = 16

=> x = 4

The legnths of the diagonals are

QS = d1 = 3x = 3 * 4 = 12 cms

PR = d2 = 2x = 2 * 4 = 8 cms