In the figure below, triangle ABC is similar to triangle PQR, as shown below: What is the length of side PQ?

A right triangle ABC with right angle at B and base BC is drawn. Length of AB is 4, length of BC is 2. 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 12.

Question

Maci Browning

Mathematics

2 February, 04:11

In the figure below, triangle ABC is similar to triangle PQR, as shown below: What is the length of side PQ?

A right triangle ABC with right angle at B and base BC is drawn. Length of AB is 4, length of BC is 2. 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 12.

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Answers (1)

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Akira Haley · Answer 1

For two polygons to be considered similar, the corresponding angles need to be congruent and at the same time, the corresponding sides sides need to be proportional.

The corresponding side of QR is BC

BC = 2 and QR = 12

As you can see QR is 6 times longer than BC and so PQ should be proportional to AB by the same factor.

if AB is 4 then multiply that by 6:

4 x 6 = 24

Line PQ is 24