Question

There are two squares such that the side of the big square is 3 cm longer than the smaller one and the area of the big square is 81 sqcm more than the smaller one.find the side of each square ?

Answer 1

Let the side of the smaller square be x cm

∴ Side of larger square = x+3 cm

Area of the smaller square = x² sq. cm

Area of the larger square = (x+3)² sq.cm

∴ ATQ,

⇒ 81 + x² = (x+3)²

⇒ 81 + x² = x² + 6x + 9

⇒ 81 -9 =  6x

⇒ 72 =  6x

⇒ 72/6 = x

⇒ 12 = x

Therefore,

Side of smaller square = x cm =  12 cm

Side of larger square = x+3 cm = 12 + 3 cm = 15cm