A circle circumscribes a rectangle whose sides are in the ratio 4 : 3. If the perimeter of the rectangle is 56 cm, then what is the area (in cm) of the circle?
Show answer & explanation
Correct answer: B
Explanation
Correct Answer is option 2 i.e. 100 π
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Concept |
Understanding |
Application |
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Perimeter of rectangle = 2(l + b) Diagonal of rectangle = √(l2+b2)
Area of circle = πr2
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Ratio of sides of rectangle = 4 : 3 Suppose sides are 4x and 3x.
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Perimeter of rectangle = 56 cm ⇒ 2(4x + 3x) = 56 ⇒ 14x = 56 ⇒ x = 4 Sides = 16 and 12 cm Since the circle is circumscribed in the rectangle; Diagonal of rectangle = Diameter of circle Now, Diagonal of rectangle = √(162 + 122) = 20 cm Diameter of circle = 20 cm Hence, radius of circle = 10 cm Area of circle = πr2 ⇒ π × 102 ⇒ 100π |