SOLUTION: One side of a triangle is 2 meters shorter than the base, and the other side is 3 meters longer than half the base. If the perimeter is 15 meters, find the length of each side

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Question 1017738: One side of a triangle is 2 meters shorter than the base, and the other side is 3 meters longer than half the base. If the perimeter is 15 meters, find the length of each side
Answer by ikleyn(52781) About Me  (Show Source):
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One side of a triangle is 2 meters shorter than the base, and the other side is 3 meters longer than half the base.
If the perimeter is 15 meters, find the length of each side.
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Let  x  be the length of the triangle base,  in meters.

Then the first side has the length of  (x-2) meters,  and the third side has the length of  x%2F2%2B3   meters. 

So the perimeter of the triangle is   x + (x-2) + %28x%2F2%2B3%29.

Thus you have an equation 

x + (x-2) + %28x%2F2%2B3%29 = 15,

according to the condition.  Multiply both sides by 2. You will get

2x +(2x-4) + (x+6) = 30.

5x + 2 = 30,

5x = 30 - 2 = 28

x = 28%2F5 = 53%2F5 = 5.6 meters.

It is the length of the base in meters.
The first side is  5.6 - 2 = 3.6 meters long,  and the third side is  5.6%2F2+%2B+3 = 2.8 + 3 = 5.8 meters.

Check. 5.6 + 3.6 + 5.8 = 15 m.

Answer.  The first side is  3.6 m long,  the second side (the base) is  5.6 m and the third side is  5.8 m.