Sprinters A, B and C traverse their respective paths at uniform speeds u, v and w respectively. It is known that u2 : v2 : w2 is equal to Area A : Area B : Area C, where Area A, Area B and Area C are the areas of triangles A1A2A3, B1B2B3, and C1C2C3 respectively.
Where would A and C be when B reaches point B3?
Explanation:
Given that u2 : v2 : w2 = Area A : Area B : Area C …(i)
∵ The area of an equilateral triangle is proportional to the square of its side,
∴ Area A : Area B : Area C = (A1A2)2 : (B1B2)2 : (C1C2)2 …(ii)
From (i) and (ii),
u : v : w = A1A2 : B1B2 : C1C2
∴ 2u : 2v : 2w = 2(A1A2) : 2(B1B2) : 2(C1C2) = (A1 to A3) : (B1 to B3) : (C1 to C3)
Thus, C and A would be at C3 and A3 respectively when B reaches B3.
Hence, option (b).
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