# 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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 Question 151919: 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. THe second longest side is 2 yards shorter than the longest side. What is the length of each side?Answer by Earlsdon(6294)   (Show Source): You can put this solution on YOUR website!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