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attashe74 [19]
3 years ago
7

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. L

ength 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
Mathematics
2 answers:
GenaCL600 [577]3 years ago
6 0

Answer: PQ = 18 unit.

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, \frac{AB}{PQ} =\frac{BC}{QR} =\frac{AC}{PR}

⇒\frac{AB}{PQ} =\frac{BC}{QR}

⇒\frac{6}{PQ} =\frac{8}{24} ( because, here, AB= 6, BC=8 and QR=24)⇒  PQ=18

MariettaO [177]3 years ago
4 0
It would be less so 6
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