The perimeter of a triangle is 33 inches. The sum of the length of the longest side and twice the length of the

Question

shortest side is 31 inches. Twice the length of the longest side minus the sum of the lengths of the other sides is
12 inches. Find the lengths of all sides.

How do I set it up and write out my equations?

Answer 1

shortest side --- x
middle size ----- y
largest side ----- z

first equation is obvious: x+y+z = 33 , #1
second equation:
"The sum of the length of the longest side and twice the length of the shortest side is 31 inches"
---> z + 2x = 31 , #2

third equation:
"Twice the length of the longest side minus the sum of the lengths of the other sides is
12 inches"
--->
2z - (x+y) = 12
2z - x - y = 12 , #3

add #1 and #2
3z = 45
z = 15

plug into #2:
15 + 2x = 31
2x = 16
x = 8

plug the two values found into #1
x+y+z= 31
8+y+15 = 33
y = 10

the sides are 8, 10, and 15

check my arithmetic