Question

the side of one square is 3cm longer than twice the side of the 2nd square. the difference in their areas is 144sq cm. find the side of two squares

Answer 1

let

x = the length of the side of the first square

y = the length of the side of the second square

the side of one square is 3 cm longer than twice the side of the second square

x = 3 + 2y

the difference in their areas is 144 cm^2

plug x = 3 + 2y into the last equation

(3 + 2y)^2 - y^2 = 144

by solving the equation we find and consider the positive roots (since the length of the side can not be a negative number)

x = 3 + 2*5

x = 13 cm

the sides of the two squares are 5 cm and 13 cm.

Answer 2

area of 1st square is =( 3 + 2x )²
= 9 + 12x + 4x²

area of second square = (2x)²

= 4x²

difference:
9 + 12x + 4x² - 4x² = 144
12x = 135
x= 45/4