Question

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

Answer 1

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Answer 2

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


x^2 - y^2 = 144


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)


y = 5 cm

x = 3 + 2*5


x = 13 cm


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