Question

The length of a rectangle is twice its breadth. If its length is decreased half of the 10 cm and the breadth is increased by half of the 10 cm cm, the area of the rectangle is increased by 5 sq cm, more than 70 sq cm. Find the length of the rectangle.

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Answer 1

Since the length of this rectangle is twice its breadth, the length is equal to 40 cm.

How to calculate the area of a rectangle?

Mathematically, the area of a rectangle can be calculated by using this formula:

Area = Length × Width

Based on the information provided, we have:

• Its length is decreased half of the 10 cm ⇒ (length - 5)

• Its breadth is increased by half of the 10 cm ⇒ (breadth + 5)

• Its area is increased by 75 cm ⇒ (area + 5)

Substituting the parameters into the formula, we have:

LB + 75 = (L - 5)(B + 5)

2B² + 75 = (2B - 5)(2B + 5)

2B² + 75 = 2B(B + 5) - 5(B + 5)

2B² + 75 = 2B² + 10B - 5B - 25

5B = 75 + 25

5B = 100

B = 100/20

B = 20 cm.

For the length, we have:

L = 2B

L = 2 × 20

L = 40 cm.

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