# Algebra 2

the perimeter of a triangle is 19 cm. if the length of the longest side is twice that of the shortest side and 3cm less than the sum of the lengths of the other two sides, find the length of the three sides

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1. shortest side ---- x
longest side ----- 2x
middle side ---- y

longest side is also x+y-3
2x = x+y-3
x = y-3
y = x+3

sum = x+2x + y = 19
x+2x+(x+3) = 16
4x=16
x = 4

shortest side = 4
longest side = 8
middle side = 7

check:
they clearly add up to 19
is the longest side equal to 3 less than the sum of the other two ?
is 8 = 4+7 - 3 ? YES

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