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In the figure below, triangle ABC is similar to triangle PQR, as shown below:

A right triangle ABC with right angle at B and base BC is drawn. Length of AB is 16, length of BC is 20. 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 80.

What is the length of side PQ?

In the figure below triangle ABC is similar to triangle PQR as shown below A right triangle ABC with right angle at B and base BC is drawn Length of AB is 16 le class=

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Angle A is congruent to angle P and angle C is congruent to angle R.
Triangle ABC  is similar to triangle PQR

AB = 16 and BC = 20
QR = 80, PQ = ?

AB/BC = PQ/QR
16/20 = PQ/80
PQ = 80 * 16 / 20
PQ = 64
fichoh

The length of the side PQ using the principle of similar triangle is 64

Using the principle of similar triangles, we can set up an expression thus :

  • AB/BC = PQ/QR

  • AB = 16 ; BC = 20 ; PQ =? ; QR = 80

Hence, we have ;

16/20 = PQ/80

cross multiply

20 × PQ = 16 × 80

20 × PQ = 1280

PQ = 1280 / 20

PQ = 64

Therefore, the value of PQ will be 64.

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