Question

A side of a square is 2 cm greater than one of the sides of a rectangle and 5 cm smaller than the other side of the rectangle. Find the area of the square, if it is known that it is 50 cm2 smaller than the area of the rectangle.

Answer 1

400 cm²

Explanation:

Let s represent the length of the side of the square in cm. Then the rectangle dimensions are (s-2) and (s+5), and the relation given by the problem statement is ...

s² = (s -2)(s +5) -50

s² = s² +3s -60 . . . . . . eliminate parentheses

3s = 60 . . . . . . . . . . . . add 60-s²

60/3 = s = 20 . . . . . . . the side length of the square is 20 cm.

The area of the square is (20 cm)² = 400 cm².

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Check

The dimensions of the rectangle are 18 cm by 25 cm, so its area is 450 cm². The area of the square is 50 cm² smaller than that, as required.