Question

In the given figure P and Q are points on the sides AB and AC respectively of triangleABC such that AP=3.5cm,PB=7cm and QC=6cmIf PQ=4.5cm,then find BC.

Answer 1

Hi...
Actually in your question u had missed one information that AQ=3cm... Please check it out...
But if AQ=3cm.. then..
solution is attached above...
Hope it helps you...

Answer 2

Correct Question:

In the given figure P and Q are points on the sides AB and AC respectively of triangle ABC such that AP=3.5cm, PB=7cm, AQ=3cm, and QC=6cm. If PQ=4.5cm, find BC.

Final Answer:

The length of side BC in the given figure, where P and Q are points on the sides AB and AC respectively of triangle ABC such that AP=3.5cm, PB=7cm, AQ=3cm, QC=6cm, and PQ=4.5cm; is 13.5cm.

Given:

In the given figure P and Q are points on the sides AB and AC respectively of triangle ABC such that AP=3.5cm, PB=7cm, AQ=3cm, and QC=6cm.

Also, PQ=4.5cm.

To Find:

The length of side BC in the given figure of triangle ABC.

Explanation:

The following points are important to arrive at the solution to the problem.

• Similar triangles have their corresponding angles and sides proportional to each other.
• Any pair of Congruent triangles are also similar triangles to each other.

Step 1 of 3

Observe the following in the triangles $\triangle PAQ,\; \triangle BAC$.

• AP=3.5cm, and $AB=AP+PB=(3.5+7)cm=10.50cm$

• AQ=3cm, and $AC=AQ+QC=(3+6)cm=9cm$
• The common angle $\angle PAQ=\angle BAC$

So, the triangles $\triangle PAQ,\; \triangle BAC$ are similar triangles.

Step 2 of 3

From similar triangles $\triangle PAQ,\; \triangle BAC$, deduce the following.

$AQ:AC=AP:AB=PQ:BC$

Step 3 of 3

Now, from the lengths AP=3.5cm, PB=7cm, AQ=3cm, QC=6cm, and PQ=4.5cm, the following is deduced.

$AQ:AC=AP:AB=PQ:BC\\3:9=3.50:10.50=4.50:BC\\\frac{BC}{4.50} =\frac{10.50}{3.50} =\frac{9}{3} \\\frac{BC}{4.50}=\frac{3}{1}\\BC=3\times4.50\\BC=13.50\;cm$

Therefore, the required length of side BC in the given figure, where P and Q are points on the sides AB and AC respectively of triangle ABC such that AP=3.5cm, PB=7cm, AQ=3cm, QC=6cm, and PQ=4.5cm; is 13.5cm.

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