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?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. 384.
We know that,
The perimeter of a square = 4 × the length of the sides
The perimeter of a rectangle = 2 × (Length + Breadth)
Area of rectangle = Length × Breadth
Calculation:
The perimeter of the square is 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 is 2x/3
Accordingly,
⇒ 2 × (x + 2x/3) = 80
⇒ 5x/3 = 40
⇒ x = 24
The length of the rectangle is 24 m and the breadth is (2/3) × 24 = 16 m
The area of the rectangle is (24 × 16) = 384 m2
Thus, The area of the rectangle is 384 m2