Question
Download Solution PDFThe length and breadth of a rectangle are in the ratio 5:3. The perimeter of the rectangle is equal to the perimeter of a square. The side of the square is equal to the radius of a circle. What is the area of the circle if the breadth of the rectangle is 12 cm?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFLet the length be 5y and the breadth be 3y.
Given breadth (3y) = 12 cm, so y = 12/3 = 4 cm.
Length = 5y = 5 × 4 = 20 cm.
Perimeter of Rectangle:
Perimeter = 2(length + breadth) = 2(20 + 12) = 2(32) = 64 cm.
Perimeter of Square:
Perimeter of square = Perimeter of rectangle = 64 cm.
Side of Square:
Side of square = Perimeter / 4 = 64 / 4 = 16 cm.
Radius of Circle:
Radius of circle = Side of square = 16 cm.
Area of Circle:
Area = π × radius² = π × 16² = 256π cm².
Thus, the correct answer is 256π cm²
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