Question

in triangle ABC . P and Q are points on side AB and AC respectively such that PQ parallel BC if AP is equal to 4 cm PB is equal to 6 cm and PQ is equal to 3 cm determine BC

Answer 1

i hope the answer is correct

Answer 2

Answer:

7.5 unit

Step-by-step explanation:

Given :

In triangle ABC,

P and Q are points on side AB and AC respectively such that PQ parallel BC,

We have to find : BC,

Since, PQ ║ BC,

By the alternate interior angle theorem,

∠APQ = ∠ ABC

∠AQP = ∠ACB

By AA similarity postulate,

Δ APQ ≅ Δ ABC,

The corresponding sides of similar triangles are in same proportion,

$\frac{AP}{AB}=\frac{PQ}{BC}$

$\frac{AP}{AP+PB}=\frac{PQ}{BC}$

We have, AP = 4 unit, PB = 6 unit and PQ = 3 unit,

$\implies \frac{4}{4+6}=\frac{3}{BC}$

$\frac{4}{10}=\frac{3}{BC}$

$\implies BC=\frac{30}{4}=7.5$