Question

The side of one square is 3 cm longer than twice of the second square the difference in their areas is 144 square centimetre find the sides of the two squares

Answer 1

Let the side length of one square be x
Then, that of other square is 2x+3
Given,
${(2x + 3)}^{2} - {x}^{2} = 144 \\ 3 {x}^{2} + 12x - 135 = 0 \\ {x}^{2} + 4x - 45 = 0 \\ (x + 9)(x - 5) = 0 \\ x = - 9 \: \: or \: \: 5 \\ since \: \: - ve \: \: value \: \: is \: \: not \: \: acceptable \\ x = 5$

Therefore, sides are 5 cm and 13 cm

Answer 2

Let the side length of one square be x

Then, that of other square is 2x+3

Given,

{(2x + 3)}^{2} - {x}^{2} = 144 \\ 3 {x}^{2} + 12x - 135 = 0 \\ {x}^{2} + 4x - 45 = 0 \\ (x + 9)(x - 5) = 0 \\ x = - 9 \: \: or \: \: 5 \\ since \: \: - ve \: \: value \: \: is \: \: not \: \: acceptable \\ x = 5

Therefore, sides are 5 cm and 13 cm