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Q132 (IAS/1998) Science & Technology › Basic Science (Physics, Chemistry, Biology) › Quantitative aptitude topics Answer Verified

LMNOP, is a semi-circle with centre at R and diameter LP, LSR and RQP are also semi-circles with centres at T and U and diameters LR = RP = 1/2 LP. The ratio of perimeters of LMNOP and LSRQP is

Result
Your answer: —  Â·  Correct: B
Explanation

Given LR = RP = (1/2)LP as stated in the problem, each small semicircle has diameter half the big semicircle’s diameter. Perimeter of a semicircle = (half circumference) + diameter = πr + 2r, where r is its radius. For the large semicircle, r_big = LP/2, so P_big = π(LP/2) + 2(LP/2) = LP(π/2 + 1). Each small semicircle has r_small = LP/4, so P_small = π(LP/4) + 2(LP/4) = LP(π/4 + 1/2). The two small semicircles together have P_combined = 2·P_small = LP(π/2 + 1), equal to P_big. Hence the ratio is 1: 1.

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