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The length of a rectangle is twice that of its breadth. The perimeter of a given rectangle is 90 cm. If length decreased by 5 cm and breadth increased by 5 cm, then the area of the rectangle increased by how much (In cm square)?

The length of a rectangle is twice that of its breadth. The perimeter of a given rectangle is 90 cm. If length decreased by 5 cm and breadth increased by 5 cm, then the area of the rectangle increased by how much (In cm square)? Correct Answer 50

Let ‘l’ be the length of a given rectangle and ‘b’ be its breadth.

Here, l = 2b (given)

Perimeter of rectangle = 2(l + b)

⇒ 2 (2b + b) = 90

⇒ 3b = 45

⇒ b = 15 cm

⇒ length l = 2b = 30 cm

Now, when length decreased by 5 cm and breadth increased by 5 cm,

Then, increase in the area of rectangle = (new area) – (old area)

= (30 – 5) * (15 + 5) – (30 * 15)

= 500 – 450

= 50 cm square

Hence, increase in the area of rectangle is 50 cm square

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