Question 1017738
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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 &nbsp;<B>x</B>&nbsp; be the length of the triangle base, &nbsp;in meters.

Then the first side has the length of &nbsp;(x-2) meters, &nbsp;and the third side has the length of &nbsp;{{{x/2+3}}} &nbsp; meters. 

So the perimeter of the triangle is &nbsp;&nbsp;x + (x-2) + {{{(x/2+3)}}}.

Thus you have an equation 

x + (x-2) + {{{(x/2+3)}}} = 15,

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

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

5x + 2 = 30,

5x = 30 - 2 = 28

x = {{{28/5}}} = {{{5}}}{{{3/5}}} = 5.6 meters.

It is the length of the base in meters.
The first side is &nbsp;5.6 - 2 = 3.6 meters long, &nbsp;and the third side is &nbsp;{{{5.6/2 + 3}}} = 2.8 + 3 = 5.8 meters.

<U>Check</U>. 5.6 + 3.6 + 5.8 = 15 m.

<B>Answer</B>. &nbsp;The first side is &nbsp;3.6 m long, &nbsp;the second side (the base) is &nbsp;5.6 m and the third side is &nbsp;5.8 m. 
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