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In the diagram, what is the perimeter of $\triangle PQR$?

 Mar 16, 2020
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Let the foot of the perpendicular dropped from Q be H.

 

In triangle HQR, we have a Pythagorean triple: 15-20-25. (like 3-4-5 but you multiply each side by 5), so QH = 15.

 

Next, in triangle PQH, we have another Pythagorean triple, 8-15-17. So, we have PQ = 17.


The perimeter is PQ + QR + PR = 17 + 25 + 28 = 70.

 Mar 16, 2020

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