Question

In $\triangle ABC$, P and Q are points on sides AB and AC respectively such that $PQ \parallel BC$. If AP = 3 cm, PB = 5 cm and AC = 8 cm, find AQ.

Answer 1

Answer:

The length of side AQ is 3 cm.

Step-by-step explanation:

Given:

In ΔABC, P and Q points lie on sides AB and AC and PQ || BC.

AP = 3 cm, PB = 5cm, AC = 8 cm.

In ΔABC, PQ || BC, Then

AP/AB = AQ/AC

[By using basic proportionality theorem]

3/(AP + PB) = AQ/8

3/(3 + 5) = AQ/8

⅜ = AQ/8

AQ = 3  

Hence, the length of side AQ is 3 cm.

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Answer 2

$\huge\Mathcal{Solution}$

Given :

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

☆ $PQ \parallel BC$.

☆ AP = 3 cm

☆ PB = 5 cm

☆ AC = 8 cm

☆ AQ = ??

Solve:

In ΔABC, PQ || BC,

Then,

$\frac{AP}{AB}= \frac{AQ}{AC}$

[By using basic proportionality theorem]

$\frac{3}{(AP + PB)} =\frac{ AQ}{8}$

$\frac{3}{(3 + 5)} =\frac{ AQ}{8}$

$\frac{3}{(8)} =\frac{ AQ}{8}$

$\frac{3}{8} \times 8 = AQ$

AQ = 3cm

Hence , The value of AQ is 3 cm.