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.

Step-by-step 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,
`(AB)/(PQ) =(BC)/(QR) =(AC)/(PR)`

⇒
`(AB)/(PQ) =(BC)/(QR)`

⇒
`(6)/(PQ) =(8)/(24)` ( because, here, AB= 6, BC=8 and QR=24)⇒ PQ=18