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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?

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? Correct Answer 40 cm

Given

Length of rectangle is twice its breadth. Length is decreased by 5 cm and breadth is increased by 5 cm. Area of rectangle is increased by 75 cm2

Concept used

Area of rectangle = Length × Breadth

Calculation

Length is twice the breadth of the rectangle.

Length = 2x

Breadth = x 

Area = 2x2 - - - (i)

Length is decreased by 5 cm and breadth is increased by 5 cm.

Area is increased by 75 cm2.

⇒ (2x - 5) (x + 5) = 2x2 + 75

⇒ 2x2 + 10x - 5x - 25 = 2x2 + 75

⇒ 5x = 100

⇒ x = 20

Length of rectangle = 2 × 20 = 40 cm

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