Question

The length of a rectangle is greater than the breadth by 3 cm. If the length is
increased by 9 cm and the breadth is reduced by 5 cm, the area remains the same
Find the dimensions of the rectangle.​

Answer 1

Let the breadth be x cm.

Then the length will be (x+3) cm.

Area of the rectangle = x(x+3) cm^2. ---------------- (1)

Given that length is increased by 9cm = x + 3 + 9 = x + 12 cm.

Given that breadth is reduced by 5cm = x - 5 cm.

Area of the rectangle = (x+12)(x-5). -------------- (2)

On solving (1) and (2), we get

x(x+3) = (x+12)(x-5)

x^2 + 3x = x^2 + 7x - 60

4x = 60

x = 15.

Breadth = 15cm.

Length = 15 + 3 = 18 cm.

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