Question : The perimeter of a square is half the perimeter of a rectangle. The perimeter of the square is 40 m. If its breadth is two-thirds of its length, then what is the area (in m2) of the rectangle?
Option 1: 384
Option 2: 196
Option 3: 321
Option 4: 400
Correct Answer: 384
Solution : Given: The perimeter of the square = 40 m The perimeter of a square is half the perimeter of a rectangle. The perimeter of the rectangle is 2 × 40 = 80 m Let, the length of the rectangle be $x$ The breadth of the rectangle = $\frac{2x}{3}$ According to the question, The perimeter of the rectangle = 80 m ⇒ $2 \times ( x + \frac{2x}{3}) = 80$ ⇒ $\frac{5x}{3} = 40$ ⇒ $x = 24$ Length of the rectangle = 24 m Breadth = $\frac{2}{3}\times 24$ = 16 m Area of the rectangle is (24 × 16) = $384\ m^2$ Hence, the correct answer is 384.
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