SOLUTION: the lengths of the sides of a triangle are 13 cm, 14 cm and 15 cm. Find the length of the altitude corresponding to longest side.

Algebra ->  Triangles -> SOLUTION: the lengths of the sides of a triangle are 13 cm, 14 cm and 15 cm. Find the length of the altitude corresponding to longest side.      Log On


   

Question 696151: the lengths of the sides of a triangle are 13 cm, 14 cm and 15 cm. Find the length of the altitude corresponding to longest side.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Maybe not the best way, but first idea that came to me.
Applying Pythagoras to both righ triangles, we get the system
system%28h%5E2%2Bx%5E2=14%5E2%2Ch%5E2%2B%2815-x%29%5E2=13%5E2%29 --> system%28h%5E2%2Bx%5E2=196%2Ch%5E2%2Bx%5E2-30x%2B225=169%29
Subtracting the second equation from the first, we get
h%5E2%2Bx%5E2-%28h%5E2%2Bx%5E2-30x%2B225%29=196-169 --> h%5E2%2Bx%5E2-h%5E2-x%5E2%2B30x-225=27 --> 30x-225=27 --> 30x=27%2B225 --> 30x=252 --> x=252%2F30 --> x=8.4
Substituting that value for x into h%5E2%2Bx%5E2=196 , we get
h%5E2%2B8.4%5E2=196 --> h%5E2%2B70.56=196 --> h%5E2=196-70.56 --> h%5E2=125.44 --> h=sqrt%28125.44%29 --> highlight%28x=11.22%29