SOLUTION: The perimeter of a triangle is 56 centimeters. The longest side is 2 centimeters less than the sum of the other two sides. Twice the shortest side is 13 centimeters less than the

Algebra ->  Triangles -> SOLUTION: The perimeter of a triangle is 56 centimeters. The longest side is 2 centimeters less than the sum of the other two sides. Twice the shortest side is 13 centimeters less than the      Log On


   

Question 990952: The perimeter of a triangle is 56 centimeters. The longest side is 2 centimeters less than the sum of the other two sides. Twice the shortest side is 13 centimeters less than the longest side. Find the lengths of each side of the triangle.
a=
b=
c=a+b-2
a+b+c=56
Found 3 solutions by macston, josgarithmetic, MathTherapy:
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
c=longest side; a=shortest side; b=middle side
.
a+b=c+2 Use this to substitute for (a+b)
.
a+b+c=56 Substitute for (a+b)
(c+2)+c=56
2c=54
c=27
ANSWER 1: Longest side is 27 centimeters
.
c-13=2a
27-13=2a
14=2a
7=a
ANSWER 2: The shortest side is 7 centimeters
.
a+b+c=56
7cm+b+27cm=56cm
b+34cm=56cm
b=22cm
ANSWER 3: the middle side is 22 centimeters.

Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
x, y, z, the sides;
x%2By%2Bz=56
Take z as the longest side; z=-2%2Bx%2By;
Take x as the shortest side; x=-13%2Bz;


This makes a system of equations
system%28x%2By%2Bz=56%2Cx=z-13%2Cz=x%2By-2%29

Maybe Row Elimination would be the way to go. Another way is substitute for x in the first and third equations, and continue to work the the two-variable system resulting. Doing this way:

system%28z-13%2By%2Bz=56%2Cz=z-13%2By-2%29

system%282z%2By=56%2B13%2C0=y-15%29

system%282z%2By=69%2Cy=15%29

Found one side length, highlight%28y=15%29.

2z%2B15=69
2z=69-15
2z=74
highlight%28z=37%29

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

The perimeter of a triangle is 56 centimeters. The longest side is 2 centimeters less than the sum of the other two sides. Twice the shortest side is 13 centimeters less than the longest side. Find the lengths of each side of the triangle.
a=
b=
c=a+b-2
a+b+c=56
Shortest side:       highlight_green%287%29 cm

Intermediate side:  highlight_green%2822%29 cm

Longest side:       highlight_green%2827%29 cm