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: PQ = 18 unit.Explanation: Since, according to question, [tex]\triangle ABC\sim\triangle PQR[/tex] .Therefore, by the property of similar triangles the ratio of corresponding sides must be equal.Here, The right angle are at A in [tex]\triangle ABC[/tex] and at Q in [tex] \triangle PQR[/tex] respectively. Moreover,  [tex]\angle A[/tex] is congruent to [tex]\angle P[/tex] and [tex]\angle C[/tex] is congruent to [tex]\angle R[/tex].Therefore, AB, BC and AC are corresponding to sides PQ, QR and PR respectively.Thus, we can write, [tex]\frac{AB}{PQ} =\frac{BC}{QR} =\frac{AC}{PR}[/tex]⇒[tex]\frac{AB}{PQ} =\frac{BC}{QR}[/tex]⇒[tex]\frac{6}{PQ} =\frac{8}{24}[/tex] ( because, here, AB= 6, BC=8 and QR=24)⇒  PQ=18