If the length of a rectangle is decreased by 4 cm and the width is increased by 5 cm, the result will be a square, the area of which will be 40 cm2 greater than the area of the rectangle. Find the area of the rectangle.

Question

Samuel Lozano

Mathematics

21 June, 19:37

If the length of a rectangle is decreased by 4 cm and the width is increased by 5 cm, the result will be a square, the area of which will be 40 cm2 greater than the area of the rectangle. Find the area of the rectangle.

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Answers (1)

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Reagan Wallace · Answer 1

Let x represent the side length of the square. Then

(x + 4) * (x - 5) + 40 = x^2

x^2 - x - 20 + 40 = x^2

20 = x

The rectangle is 15 cm by 24 cm, and its area is 360 cm^2.