Given below is a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements is sufficient to answer the question. You should use the given data and your knowledge of Mathematics to choose between the possible answers.
Area of a rectangle is twice the area of a circle. What is the ratio of length and breadth of rectangle?
I. Radius of circle is equal to breadth of rectangle.
II. Perimeter of rectangle is equal to circumference of circle.
Solution
Correct Answer: Option A
Let length and breadth of rectangle be L and B, respectively. Let radius of circle be R.
Area of a rectangle is twice the area of a circle.
⇒ LB = 2π R2
From statement I:
Radius of circle is equal to breadth of rectangle.
⇒ R = B
⇒ LB = 2π B2
⇒ L = 2π B
⇒ Ratio of length and breadth can be found.
∴ Statement I alone is sufficient to answer the question.
From statement II:
Perimeter of rectangle is equal to circumference of circle.
⇒ 2(L + B) = 2π R
⇒ (L + B) = π R
Also, LB = 2π R2
⇒ LB/2π = (L+B)2/π2
⇒ π LB = 2L2 + 2B2 + 4LB
Divide equation by B2, and put L/B = T
⇒ 2T2 + (4–π)T + 2 = 0
Discriminant of this equation is negative and hence no real roots exist.
∴ Statement II alone is not sufficient to answer the question.
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