SOLUTION: In the △PQR, PQ = 39 in, PR = 17 in, and the altitude PN = 15 in. Find QR. QR can be (x) in or (y) in. Find: x and y

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Question 1065916: In the △PQR, PQ = 39 in, PR = 17 in, and the altitude PN = 15 in. Find QR.
QR can be (x) in or (y) in.
Find: x and y
Found 2 solutions by ikleyn, KMST:
Answer by ikleyn(52855)   (Show Source): You can put this solution on YOUR website!
.
Make a sketch. 

Find two right-angled triangles.

For each of these two right-angled triangles you have given a hypotenuse and one of the two legs.

Apply the Pythagorean theorem and find the second leg for each of the two right-angled triangles.


Then two options are possible:

a) QR is the sum of lengths of these legs,   or

b) QR is the difference (if the original triangle is obtuse).


Answer by KMST(5328)   (Show Source): You can put this solution on YOUR website!
, or some mirror images.
Applying the Pythagorean theorem to right triangles PNQ and PNR, we get
and .
Substituting the known lengths
(I will not write units, but we know all the lengths were measured in inches),
--->--->--->--->
and
--->--->--->---> .
So depending on which of the two drawings represents triangle PQR,
either
or .
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