The length of a recta

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Question

The length of a rectangle is twice its breadth. If its length is decreased by 5 cm and breadth is increased by 5 cm, the area of the rectangle is increased by 75 sq.cm. What is the length of the rectangle?

Options:

A . 18 cm

B . 16 cm

C . 40 cm

D . 20 cm

Answer: Option C

Answer : Option C

Explanation :

Let breadth = x cm
Then length = 2x cm
Area = lb = x Ã— 2x = 2x²
New length = (2x - 5)
New breadth = (x + 5)
New Area = lb = (2x - 5)(x + 5)
But given that new area = initial area + 75 sq.cm.
=> (2x - 5)(x + 5) = 2x² + 75
=> 2x² + 10x - 5x - 25 = 2x² + 75
=> 5x - 25 = 75
=> 5x = 75 + 25 = 100
=> x = ¹⁰⁰/₅ = 20 cm

Length = 2x = 2 × 20 = 40cm

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