In the △PQR, PQ = 39 in, PR = 17 in, and the altitude PN = 15 in. Find QR.

Accepted Solution

Answer:So, this triangle PQR can be broken into two right triangles, PNQ and PNR, with legs PQ = 39, PN =15, and QN = ? and PR = 17, PN = 15, and NR =? respectively.
Let's solve for what is easier first: Since we know that 5-15-17 is a Pythagorean triplet, we can infer that NR is 5....like I said earlier, it is a right triangle, so this guess holds true.
Here comes the interesting part:Now, we have one part of QR, which is QN.The other part can be solved by using the Pythagorean theorem.It is (39^2-15^2)^(1/2)..which gives you 36, the square root of 1296, which happens to be the difference between the squares of 15 and 39.SO, QR = QN + NR5+36 = 41QR = 41.Hope this helps!