SOLUTION: The perimeter of a triangle is 71 71 cm. The longest side is 5 5 cm less than the sum of the other two sides. Twice the shortest side is 5 5 cm less than the longest side.

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Question 1132250: The perimeter of a triangle is
71
71 cm. The longest side is
5
5 cm less than the sum of the other two sides. Twice the shortest side is
5
5 cm less than the longest side. Find the length of each side of the triangle.
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
Assume the problems is:
:
The perimeter of a triangle is 71 cm.
a + b + c = 71
The longest side is 5 cm less than the sum of the other two sides.
a = b + c - 5
or
a - b - c = -5
Twice the shortest side is 5 cm less than the longest side.
2c = a - 5
Find the length of each side of the triangle.
:
Use elimination on the first two equations
a + b + c = 71
a - b - c = -5
-----------------Addition eliminates b and c, find a
2a + 0 + 0 = 66
a = 66/2
a = 33 cm is the longest side
then
using the 3rd equation
2c = 33-5
2c = 28
c = 28/2
c = 14 cm is the shortest side
:
Using the 2nd equation
33 = b + 14 - 5
33 = b + 9
b = 33 - 9
b = 24 cm is the middle side
;
;
See if that checks out
33 + 24 + 14 = 71