A rectangle is such that its area is 48 cm2 and its perimeter is 28 cm. If a rhombus is formed by joining the midpoints of the sides of this rectangle, what is the area of the rhombus?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 24 cm2.
Let the rectangle length = l cm and breadth = b cm
Area of rectangle = lb = 48
Perimeter of rectangle = 2(l + b) = 28 ⇒ l + b = 14
Since 8 × 6 = 48, 8 + 6 = 14: l = 8 cm and b = 6 cm
Joining the midpoints of the sides of a rectangle gives a rhombus whose diagonals are equal to the length and breadth of the rectangle.
Area of rhombus = (1/2) × d1 × d2, where d1 = l = 8 cm and d2 = b = 6 cm
Area = (1/2) × 8 × 6 = 24 cm2