math
posted by Toni on .
the perimeter of a triangle is 54 centimeters. the longest side is 6 centimeters less than the sum of the other two sides. Twice the shortest side is 10 centimeters less than the longest side. Find the lengths of each side of the tirangle

shortest side  x
longest  2x + 10
let middle side be y
2x + 10 = x + y 6
y = x+16
so x + 2x+10 + x+16 = 54
4x = 28
x = 7
shortest side = 7
longest side = 24
middle side = 23
check: is the sum = 54 ? yes!
is 24 equal to 6 less than 30 ?, yes
is twice 7 10 less than 24 ? yes!
All is good!