SOLUTION: Please help me solve this problem: One side of triangle is one-third the longest side. The third side is 7 feet less than the longest side. The perimeter is 77. Find all three

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Please help me solve this problem: One side of triangle is one-third the longest side. The third side is 7 feet less than the longest side. The perimeter is 77. Find all three       Log On


   

Question 912169: Please help me solve this problem:
One side of triangle is one-third the longest side. The third side is 7 feet less than the longest side. The perimeter is 77. Find all three sides.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
let's sides be a, b, and c where c is the longest side

One side of triangle,a, is one-third the longest side c => a=%281%2F3%29c

The third side,b, is 7ft less than the longest side c => b=c-7ft
The perimeter P=77ft.
solution:
P=77ft .... since P=a%2Bb%2Bc we have
77ft=a%2Bb%2Bc ......substitute a=+%281%2F3%29c and b=+c-7ft


77ft=%281%2F3%29c%2B%28c-7ft%29%2Bc
77ft=c%2F3%2Bc-7ft%2Bc
77ft%2B7ft=c%2F3%2B2c
84ft=%28c%2B6c%29%2F3
3%2A84ft=c%2B6c
252ft=7c
252ft%2F7=c
highlight%2836ft=c%29

now find
a=+%281%2F3%29c and b=+c-7ft
a=+%281%2F3%29c =>a=+%281%2F3%2936ft =>highlight%28a=+12ft%29
b=+c-7ft =>b=36ft-7ft =>highlight%28b=+29ft%29

check:
77ft=a%2Bb%2Bc
77ft=12ft%2B29ft%2B36ft
77ft=77ft