Hi, there--

PROBLEM:
A triangle has a perimeter of 102 in. The shortest side measures 6 inches less than the 
middle side. The longest side is 4 less than twice the middle side. Find the lengths of all 
three sides. 

SOLUTION:
Let x be the length of the middle side.

The shortest side is 6 inches less than the middle side, or x-6.

The longest side is 4 less than twice the middle side, or 2x-4.

The perimeter (the sum of the side lengths) is 102, so

x + (x-6) + (2x-4) = 102

Solve for x to find the length of the middle side. Combine like terms: x+x+2x is 4x, and
-6 + -4 is -10.

4x - 10 = 102

Add 10 to both sides.
4x = 112.

Divide both sides by 4.
x = 28

The middle side is 28 inches.
The shortest side is 6 inches less, or 22 inches,
The longest side is 4 less than twice 28, or 52 inches.

Check that the sum of these side lengths is 102 inches.
28 + 22 + 52 = 102. Check!

That's it,
Ms. Figgy