The length of a rectangle is twice the diameter of a circle. The circumference of the circle is numerically equal to the area of a square of side 22 cm. What is the breadth of the rectangle if its perimeter is 668 cm?
Solution
Correct Answer: Option B
Let the length and the breadth of the rectangle are l and b respectively.
We know that, formulae:
→ Perimeter of a rectangle = (length + breadth) × 2
→ Circumference of a circle = 2πr
Where, r = radius of the circle
Now, according to the question,
2(l + b) = 668
∴ l +b=334
∴ l = (334-b)
And, length of the rectangle =Twice the diameter of the circle
⇒ 334 – b=2×d=2× 2r=4r
∴ r=(334–b)/4
Area of square =circumference of circle,
⇒ (22)2=2πr
\(\Rightarrow {\rm{}}484 = \frac{{2 \times 22\left( {334 - b} \right)}}{{7 \times 4}}\therefore 334 - b = \frac{{484 \times 7 \times 4}}{{2 \times 22}} = 308\)
∴ b=334 – 308=26cm.
Hence, the required answer is 26 cm.
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