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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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- 30 cm
- 40 cm
- 21 cm
- 45 cm
- None of the above
Correct Option: B
Given that, l = 2b [Here l = length and b = breadth]
Decrease in length = Half of the 10 cm = 10/2 = 5 cm
Increase in breadth = Half of the 10 cm = 10/2 = 5 cm
Increase in the area = (70 + 5) = 75 sq cm
According to the question,
(l - 5) (b + 5) = lb + 75
⇒ (2b - 5) (b + 5) = 2b2 + 75 [since l = 2b]
⇒ 5b - 25 = 75
⇒ 5b = 100
∴ b = 100/ 5 = 20
∴ l = 2b = 2 x 20 = 40 cm
