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# 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

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Answer: PQ = 18 unit.Explanation: Since, according to the question, .Therefore, by the property of similar triangles the ratio of corresponding sides must be equal.Here, The right angle is in A and Q respectively. In addition, it is consistent with and is consistent .Therefore, AB, BC and AC are corresponding sides PQ, QR and PR, respectively.Therefore, we can write, ⇒⇒ ( because, here, AB= 6, BC=8 and QR=24)⇒ PQ=18