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The three sides of a triangle are n, 3n−6, and 4n−11. If the perimeter of the triangle is 39 inches, what is the length of each side? A) 5 inches, 9 inches, 25 inches B) 6 inches, 9 inches, 24 inches C) 7 inches, 10 inches, 22 inches D) 8 inches, 11 inches, 20 inches

User Szuflad
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1 Answer

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To answer this question, we start by understanding that the perimeter of a triangle is the sum of the lengths of its three sides.

Given that the three sides of this triangle are defined as n, 3n-6, and 4n-11, we combine these three expressions and set it equal to the perimeter of the triangle which is 39 inches. That gives us the equation, n + (3n - 6) + (4n - 11) = 39.

Next, we simplify this equation by adding together like terms. Combining the n terms gives 8n and combining the constant terms (-6 and -11) gives -17. This results in the simplified equation, 8n - 17 = 39.

From there, we solve for n. Start by isolating the n term, so we add 17 to both sides of the equation which gives 8n = 39 + 17 = 56. Finally, we divide by 8 to solve for n which gives us n = 56 / 8 = 7 inches. This is the length of the first side.

Substitute the value of n into the expressions for the other two sides, to compute their lengths.

The length of the second side = 3n - 6 = 3*7 - 6 = 15 inches.
The length of the third side = 4n - 11 = 4*7 - 11 = 17 inches.

So, the lengths of the three sides of the triangle are 7 inches, 15 inches, and 17 inches respectively. On comparing these lengths with the given options, we observe that none of the provided options match this solution.

Hence, the answer is 'None of the options match.'

User Alysson Myller
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