Question

In the figure below, triangle ABC is similar to triangle PQR: A right triangle ABC with right angle at B and base BC is drawn. Length of AB is 6, length of BC is 8. A similar right triangle; triangle PQR, which is triangle ABC enlarged and reflected across a horizontal line, is drawn near it. The right angle is at Q. Angle A is congruent to angle P and angle C is congruent to angle R. The length of QR is 24. What is the length of side PQ? 18 4 32 6

Answer 1

Answer: PQ = 18 unit.

Explanation: Since, according to question, $\triangle ABC\sim\triangle PQR$ .

Therefore, by the property of similar triangles the ratio of corresponding sides must be equal.

Here, The right angle are at A in $\triangle ABC$ and at Q in $\triangle PQR$ respectively.

Moreover,  $\angle A$ is congruent to $\angle P$ and $\angle C$ is congruent to $\angle R$.

Therefore, AB, BC and AC are corresponding to sides PQ, QR and PR respectively.

Thus, we can write, $\frac{AB}{PQ} =\frac{BC}{QR} =\frac{AC}{PR}$

⇒$\frac{AB}{PQ} =\frac{BC}{QR}$

⇒$\frac{6}{PQ} =\frac{8}{24}$ ( because, here, AB= 6, BC=8 and QR=24)⇒  PQ=18