Question

A right triangle ABC with right angle at B and base BC is drawn. Length of AB is 12, length of BC is 11.5. 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 34.5.

What is the length of side PQ?

12
35
33
36

Answer 1

answer has to be 36. :)

Answer 2

Option D is correct.

Length of PQ is 36 unit.

Step-by-step explanation:

If the measures of two sides in one triangle are proportional to the corresponding sides in the another triangle and their including angles are congruent, then the triangles are similar.

Given: Right angle triangle ABC at B , Length of AB = 12 unit and length of BC = 11.5 unit and in right angle triangle PQR at Q , length of QR = 34.5 unit.

Also it is given that Angle A is congruent to angle P and angle C is congruent to angle R.

To find the length of QR:

It is given that ΔABC and ΔPQR are Similar triangle

then, by the definition of similar triangle:

`(PQ)/(AB) = (QR)/(BC)`

Substitute the value of AB, QR and BC to solve for PQ;

`(PQ)/(12)=(34.5)/(11.5)` or

`PQ = (34.5 * 12)/(11.5)`

On simplify:

`PQ = 3 * 12 = 36`

Therefore, the length of side PQ is 36 units.