Question 882997: the perimeter of a triangle is 42 inches. the second side is 1 inch more than twice the first side, and the third side is 1 inch less than three times the first side. Find the lengths of the three sides of the triangle.
Answer by Leaf W.(135)   (Show Source):
You can put this solution on YOUR website! Hello!
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Let us call the first side x.
Since "the second side is 1 inch more than twice the first side," we can represent the second side as 2x + 1
Since "the third side is 1 inch less than three times the first side," we can represent the third side as 3x - 1
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The perimeter of the triangle is 42 inches, so we can create the following equation:
first side + second side + third side = 42
x + (2x + 1) + (3x - 1) = 42
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Now, just simplify and solve for x!
x + 2x + 1 + 3x - 1 = 42
Add like terms: 6x + 0 = 42
6x = 42
Divide both sides by 6: x = 7
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Therefore, the length of the first side is 7 inches. Thus, the second side is 2x + 1 = 2(7) + 1 = 14 + 1 = 15 inches, and the third side is 3x - 1 = 3(7) - 1 = 21 - 1 = 20 inches.
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The three sides of the triangle must then be 7 inches, 15 inches, and 20 inches.
I hope this helps! =)
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