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Question
The perimeter of a rectangle is 40 m. Its length is four metres less than five times its breadth. Find the area of the rectangle.
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Solution
Let breadth of the rectangle = x
Then, length of the rectangle = 5x – 4
We know that,
Perimeter of rectangle = 2(l + b)
⇒ 40 = 2(l + b) ...[∵ Perimeter = 40 m, given]
⇒ 40 = 2(5x – 4 + x)
⇒ 40 = 2(6x – 4)
⇒ 12x – 8 = 40
⇒ 12x = 40 + 8
⇒ 12x = 48
⇒ x = `48/12` = 4
So, breadth = x = 4 m and length = 5x – 4 = 5 × 4 – 4 = 16 m
∴ Area of rectangle = l × b = 4 × 16 = 64 m2
Hence, the area of rectangle is 64 m2.
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