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Question
The perimeter of a square plot of land is 64m. The area of a nearby rectangular plot is 24m2 more than the area of the given square. If the length of the rectangle is 14m, find its breadth.
Solution
The perimeter of a square with side s = P = 4s
∴ Here, the perimeter of the square 64m
Let the side of the square = s
∴ 4s = 64
⇒ s = 16m
We know, The area of a square with side s = s2
∴ s2
= 162
= 256m2
∴ The area of the rectangle
= 256 + 64
= 280m2
The area of a rectangle with length l and breadth b = A = l x b
Here, l = 14m, let breadth = b
The area of a rectangle with length 4 and breadth b = A = 14 x b
⇒ 14b = 280
⇒ b =
= 20m.
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