Single correct option
ABCD is a square of side 10 cm. E is the midpoint of side BC. The segment AE intersects the diagonal BD at point F. What is the area of triangle BEF?
- A. 10 cm²
- B. 50/3 cm²
- C. 25/3 cm²
- D. 25/4 cm²
Show answer and solution
Answer: (C) 25/3 cm²
Place A(0, 0), B(10, 0), C(10, 10), D(0, 10); then E = (10, 5).
Triangles AFD and EFB are similar (AD ∥ BE), with ratio AD : EB = 10 : 5 = 2 : 1. So F divides AE in the ratio 2 : 1, giving F = (2/3)E = (20/3, 10/3).
Triangle BEF has base BE = 5 along the line x = 10 and height = horizontal distance of F from that line = 10 − 20/3 = 10/3.
Area = (1/2) × 5 × 10/3 = 25/3 cm².
Triangles AFD and EFB are similar (AD ∥ BE), with ratio AD : EB = 10 : 5 = 2 : 1. So F divides AE in the ratio 2 : 1, giving F = (2/3)E = (20/3, 10/3).
Triangle BEF has base BE = 5 along the line x = 10 and height = horizontal distance of F from that line = 10 − 20/3 = 10/3.
Area = (1/2) × 5 × 10/3 = 25/3 cm².
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