Question

In $\triangle ABC$, P and Q are points on sides AB and AC respectively such that $PQ \parallel BC$. If AP = 4 cm, PB = 6 cm and PQ = 3 cm, determine BC.

Answer 1

Answer:

The length of BC is 7.5 cm  .

Step-by-step explanation:

Given :  

In ∆ ABC, P and Q are points on sides AB and AC and PQ || BC [/tex]. AP = 4 cm, PB = 6 cm and PQ = 3 cm

In ΔAPQ  and ΔABC

∠APQ =∠B        [corresponding angles]

∠PAQ =∠BAC   [common]

ΔAPQ∼ΔABC  

[By AA Similarity criterion]

AP/AB = PQ/BC

[Corresponding sides of two similar triangles are proportional]

4/10 = 3/BC

4 BC = 3 × 10

BC = 30/4 = 15/2

BC = 7.5 cm  

Hence, the length of BC is 7.5 cm  

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Answer 2

$\huge\bf\underline\mathcal\purple{Solution}$

Given :

In $\triangle ABC$, P and Q are points on side AB and AC respectively .

☆ $PQ \parallel BC$

☆ AP = 4 cm .

☆ PB = 6 cm .

☆ PQ = 3 cm .

☆ BC = ?

Solve :

In $\triangle\: APQ\: and\: \triangle\: ABC$

=> $\angle APQ = \angle ABC$(Corresponding angles )

and $\angle PAQ = \angle BAC$(Common)

=>$\triangle APQ ~\triangle ABC$ (By AA similarity )

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

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

$= > \frac{4}{4 + 6} = \frac{3}{bc}$

$= > 4bc = 3 \times 10$

$= > BC = \frac{30}{4}$

$= > BC= \frac{15}{2}$

$= > BC= 7.5cm$

Hence , BC = 7.5 cm .