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.

The dimensions of the rectangle can be obtained by using the quadratic

formula.

Let x represent the length of the rectangle, and y represent the width of

the rectangle.

x - 4 = y + 5 (sides of a square)

(x - 4) × (y + 5) = 40 cm²

Which gives;

(y + 5) × (y + 5) = 40 cm²

y² + 10·y + 25 = 40

y² + 10·y + 25 - 40 = 0

y² + 10·y - 15 = 0

Solving by using the quadratic formula gives;

Using the positive values for the width, we have;

y = -5 + 2·√(10)

Which gives;

x - 4 = 5 + -5 + 2·√(10) = 2·√(10)

x = 4 + 2·√(10)

The area of the rectangle, A = x × y

Therefore;

A = (-5 + 2·√(10)) × (4 + 2·√(10)) = 20 - 2·√(10)

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