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

Algebra ->  Triangles -> 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       Log On


   

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(52852) About Me  (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) About Me  (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
PN%5E2%2BNR%5E2=PR%5E2 and PN%5E2%2BNQ%5E2=PQ%5E2 .
Substituting the known lengths
(I will not write units, but we know all the lengths were measured in inches),
15%5E2%2BNR%5E2=17%5E2--->225%2BNR%5E2=289--->NR%5E2=289-225--->NR%5E2=64--->NR=8
and
15%5E2%2BNQ%5E2=39%5E2--->225%2BNQ%5E2=1521--->NQ%5E2=1521-225--->NQ%5E2=1296--->NQ=36 .
So depending on which of the two drawings represents triangle PQR,
either QR=NQ%2BNR=36in%2B8in=highlight%2844in%29
or QR=NQ-NR=36in-8in=highlight%2828in%29 .