The first side of a triangle is 3 inches shorter than the second side, and 2 inches longer than the third side. How long is each side, if the triangle has a perimeter of 28 inches?
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Let x be the first side.
Since x is 8 in. shorter than the second side, we know that we'd need to add 8 to x to get the length of the second side. So the second side is x+8. (Think, if the first side is 2 inches and it is 8 inches shorter than the second side, the second side must be 10 inches, so this works.)
The third side is 4 times the length of the first side, so the third side is 4x.
Perimeter is the sum of the sides, so: (x)+(x+8)+4x=6x+8
We also know the perimeter is 26, so we have:
6x+8=26
subtract 8:
6x=18
divide:
x=3.
The three sides have length: 3, 11, and 12.
The longest side is 12 inches long.
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