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Perimeter of Triangle Word Problem

Q: The longest side of a triangle is four inches longer than the shortest side. The remaining side is two inches longer than the shortest side. The perimeter of the triangle ( the sum of the lengths of the sides) is 24 inches. what is the length of the longest side?

A: Let x = shortest side
Let y = middle side
Let z = longest side

z = x+4
y = x+2

The perimeter is 24 inches:

P = x+y+z
24 = x+y+z

Now plug in the information y = x+2 and z = x+4:

24 = x+ x+2 + x+4
24 = 3x +6
18 = 3x
x=6

y=x+2
y=6+2
y=8

z=6+4
z=10

x=6
y=8
z=10