SOLUTION: Tom's uncle owns a triangular piece of land. The perimeter fence that surrounds the land measures 378 yards. The shortest side is 30 yards longer than one-half of the longest side.

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Let's start by assigning letters to the three sides.
A = longest side.
B = second longest side.
C = shortest side.
The problem says that the perimeter (A+B+C) is 378 yards, so you can write:

The problem also states that the shortest side, (C), is 30 yards longer than one half of the longest side, (A), so you can express this as:

And, according to the problem statement, the second longest side (B) is 2 yards shorter than the longest side, so...

Now you can make the following substitutions into the first equation:

For B substitute A-2 and for C substitute , to get:
Simplify and solve for A. Multiply through by 2 to clear the fraction.
Combine like-terms.

Subtract 56 from both sides.
Divide both sides by 5.







The sides are:
A (the longest side) = 140 yards.
B (the second longest side) = 138 yards.
C (the shortest side) = 100 yards.
Let's see if these add up to the given perimeter.
140+138+100 = 378