Question

Three straight lines are drawn through a point M, lying in the interior of triangle ABC, parallel to its sides. The areas of the resulting three triangles see Fig. are S₁, S₂ and S₃. The area of triangle ABC is

(A)  S₁ + S₂ + S₃

(B)  (√S₁ + √S₂ + √S₃)²

(C)  (S₁ + S₂ + S₃)^3/2/(S₁ + S₂ + S₃)

(D) None of these

Answer 1

Correct option (B)  (√S₁ + √S₂ + √S₃)²

See Fig.

S = (√S₁ + √S₂ + √S₃)² where S is area of ΔABC