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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 meters.
So the perimeter of the triangle is x + (x-2) + .
Thus you have an equation
x + (x-2) + = 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 = = = 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 = 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.