SOLUTION: The perimeter of a scalene triangle is double the length of the longest side. The long side is 4 more than 4 times the short side. The middle side is 8 units less than the long s

Algebra ->  Equations -> SOLUTION: The perimeter of a scalene triangle is double the length of the longest side. The long side is 4 more than 4 times the short side. The middle side is 8 units less than the long s      Log On


   

Question 913807: The perimeter of a scalene triangle is double the length of the longest side. The long side is 4 more than 4 times the short side. The middle side is 8 units less than the long side. Find the length of all the sides.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
x, short side
y, mid side
z, longest side
perimeter, x+y+z

system%28x%2By%2Bz=2z%2Cz=4%2B4x%2Cy=-8%2Bz%29

Substitute for z in the perimeter and y equations and simplify (steps not shown here):

Resulting system,
system%283x-y=-4%2C4x-y=4%29
Subtracting one equation from the other, find that highlight%28x=8%29.

Use x to find value of z:
z=4%2B4%2A8
z=32%2B4
highlight%28z=36%29

Use that z to find y value:
y=z-8
y=36-8
highlight%28y=28%29

Side lengths from shortest to longest: 8, 28, 36.