A survey of triangle ABC records a segment DE, with D on AB and E on AC, running parallel to BC. The measurements are DE = 4 cm, BC = 10 cm and AB = 15 cm. Find DB (in cm).

Question

Accepted Answer

9. Triangle ADE is similar to triangle ABC, so AD/AB = DE/BC = 4/10 = 2/5. Then AD = 2/5 × 15 = 6 cm, and DB = AB − AD = 15 − 6 = 9 cm. The answer 6 stops at AD and forgets to subtract; 7.5 halves AB as if D were the midpoint; 4 copies DE, treating the parallel segment as if it were part of AB.

A survey of triangle ABC records a segment DE, with D on AB and E on AC, running parallel to BC. The measurements are DE = 4 cm, BC = 10 cm and AB = 15 cm. Find DB (in cm).

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 10 Basic Proportionality Theorem practice