The longest side is 2 inches longer than the middle side. The shortest side is 14 inches shorter than the middle side. If the perimeter of the piece is 60 inches, what is the length of each side?
You don't say what kind of a figure you have, but since you only mentioned three sides, I will assume you have a triangle.
middle side ---- x
shortest side ---- x-14
longest side ----- x+2
x + x-14 + x+2 = 60
solve for x, sub back into my definitions.
Check if your answers fit the data
To solve this problem, let's assign variables to the unknown lengths of the sides.
Let:
x = length of the middle side
x + 2 = length of the longest side (since it is 2 inches longer than the middle side)
x - 14 = length of the shortest side (since it is 14 inches shorter than the middle side)
The perimeter of a triangle is the sum of the lengths of its sides. In this case, the perimeter is 60 inches. Therefore, we can set up the equation:
x + (x + 2) + (x - 14) = 60
Now, let's solve for x:
3x - 12 = 60
3x = 72
x = 24
Now that we have the value of x, we can substitute it back into the expressions for the lengths of the sides:
The middle side: x = 24 inches
The longest side: x + 2 = 24 + 2 = 26 inches
The shortest side: x - 14 = 24 - 14 = 10 inches
So the lengths of the sides are 10 inches, 24 inches, and 26 inches.