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Alexandra [31]
2 years ago
9

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 trian

gle; 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

Mathematics
2 answers:
expeople1 [14]2 years ago
8 0

Answer:

Option D is correct.

Length of PQ is 36 unit.

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:

\frac{PQ}{AB} = \frac{QR}{BC}

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

\frac{PQ}{12}=\frac{34.5}{11.5} or

PQ = \frac{34.5 \times 12}{11.5}

On simplify:

PQ = 3 \times 12 = 36

Therefore, the length of side PQ is 36 units.





Dahasolnce [82]2 years ago
5 0
Answer has to be 36. :)

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