SOLUTION: QT and PM are altitude of ∆PQR. If |QR| = 8cm, |PR| = 7cm and QT = 4cm, what is |PM|

Algebra ->  Trigonometry-basics -> SOLUTION: QT and PM are altitude of ∆PQR. If |QR| = 8cm, |PR| = 7cm and QT = 4cm, what is |PM|       Log On


   

Question 1132555: QT and PM are altitude of ∆PQR. If |QR| = 8cm, |PR| = 7cm and QT = 4cm, what is |PM|
Answer by ikleyn(52864) About Me  (Show Source):
You can put this solution on YOUR website!
.
QR is the side with the altitude PM.

PR is the side with the altitude QT.


You can calculate the area of the triangle PQR by two ways.


One way is      Area = 1%2F2.abs%28QR%29.abs%28PM%29.


Another way is  Area = 1%2F2.abs%28PR%29.abs%28QT%29.


Since the area is the same, it gives you an equation


    1%2F2.abs%28QR%29.abs%28PM%29 = 1%2F2.abs%28PR%29.abs%28QT%29,   or   abs%28QR%29.abs%28PM%29 = abs%28PR%29.abs%28QT%29.


Hence,  |PM| = %28abs%28PR%29%2Aabs%28QT%29%29%2Fabs%28QR%29 = %287%2A4%29%2F8 = 3.5 cm.     ANSWER

Solved.