Question : The perimeter of a square is the same as the perimeter of a rectangle. The perimeter of the square is 40 m. If its breadth is two-thirds of its length, then the area (in m2) of the rectangle is:
Option 1: 121
Option 2: 96
Option 3: 100
Option 4: 84
Correct Answer: 96
Solution :
The perimeter of the square is 40 m.
Now,
Perimeter of rectangle = 2(Length + breadth)
⇒ The perimeter of the square = Perimeter of the rectangle
⇒ 40 = $2({\text{length}}+\frac{2}{3}\text{length})$
⇒ 40 = $2(\frac{5}{3}\text{length})$
⇒ Length = $\frac{40×3}{10}$ = 12 m
So, Breadth = $\frac{2}{3}$ × 12 = 8 m
⇒ Area of rectangle = Length × Breadth = 12 × 8 = 96 m
2
Hence, the correct answer is 96.
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