SOLUTION: find the area of triangle whose sides are 5 cm ,12 cm & 13 cm. also find the length of the shortest altitude.

Algebra ->  Triangles -> SOLUTION: find the area of triangle whose sides are 5 cm ,12 cm & 13 cm. also find the length of the shortest altitude.      Log On


   

Question 316471: find the area of triangle whose sides are 5 cm ,12 cm & 13 cm. also find the length of the shortest altitude.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Use Heron's theorem,
s=%281%2F2%29%28a%2Bb%2Bc%29=%281%2F2%29%285%2B12%2B13%29=15
A=sqrt%28s%28s-a%29%28s-b%29%28s-c%29%29
A=sqrt%2815%2815-5%29%2815-12%29%2815-13%29%29
A=sqrt%2815%2810%29%283%29%282%29%29
A=sqrt%28900%29
highlight%28A=30%29
.
.
.
Then use the area of a triangle,
A=%281%2F2%29bh=30
Smallest h would have the largest b.
Use b=13.
%281%2F2%29%2813%29h=30
highlight%28h=60%2F13%29