Question

The first side of a triangle is 2 inches shorter than three times the second side. The third side is 1 inch longer than twice the second side. If the perimeter of the triangle is 101 inches, how long is each side?
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Answer 1

Answer:

The perimeter of a triangle is 74 inches. The second side is 2 inches more than twice the first side, and the third side is 6 inches less than three times the first side. Find the lengths of the three sides of the triangle.

Length of Sides (in inches)

Let's call the first side x.

Then, the problem says:

The second side is 2 inches more than twice the first side:

Second side = 2x+2

and the third side is 6 inches less than three times the first side:

Third side = 3x-6

The perimeter is the sum of the lengths of all sides, so in this case we get:

x+2x+2+3x-6 = 74 Add all x on left and also add 2 and -6:

6x-4 = 74 Add 4 on both sides

6x = 78 Divide both sides by 4:

x = 13 is the first side

Second side 2(13)+2

Third side 3(13)-6

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