A running track is comprised of a rectangular shape with semicircles at each of its shorter ends. The combined area of the two semicircles is 50% of the area of the central rectangular section. What is the approximate ratio of the length of the rectangular section to its width? (Use π=3.14)
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Correct answer: B
Explanation
Let the rectangular part have:
Length = L
Width = 2r
Area of the rectangle = L × 2r
Combined area of both semicircles = Area of 1 full circle = πr²
πr² = 50% × (2rL)
πr² = rL
L = πr
L : Width = πr : 2r = π : 2
= 3.14 : 2
= 1.57 : 1