The three sides of a triangle are n, 3n−1, and 2n+1. If the perimeter of the triangle is 42 inches, what is the length of each side?

Answer:

Step-by-step explanation:

n + 3n - 1 + 2n + 1 = 42

6n = 42

n = 7

s1 = 7 inch

s2 = 20 inch  = 3(7) - 1

s3 = 15inch  = 2(7) + 1

Answer:

THe total is 6n + 14 = 50

                  6n = 36

                   n = 6

                   6, 21, and 23

Step-by-step explanation:

To solve for the perimeter of a triangle, you have to add up all of the sides of the triangle. In the given problem, the sides are n, 3n+3, and 2n+11 (I wish I had a whiteboard to draw the picture for you). The problem also tells you what the perimeter is, 50 inches. So, all you have to do is write an equation and solve for n:

First, add all the side lengths together. n + 3n + 3 + 2n + 11. If you combine the like terms (the ones that all have a variable of n and the ones that don't), you get n + 3n + 2n + 3 + 11. Remember that "n" is the same as 1n, so 1n + 3n + 2n is 6n, and 3 + 11 is 14, so your sum is 6n + 14.

Next, make the sum from the first step equal to the perimeter the problem told you. So, write: 6n + 14 = 50

Last, solve for n. You have to get the variable n by itself, so first you move the 14 to the other side of the equation by subtracting it from both sides. You should then have 6n = 50 - 14. Combine the 50 -14 and you get 6n = 36. You still need to get the variable n by itself, so we need to get rid of the 6 that is next to it. To move the 6, you have to divide both sides by 6 so that the 6 on the left side will cancel out and you'll be left with n = 36/6 or n = 6.

Remember that this was a word problem, so your answer usually needs to be written in words and it needs to answer the question. Go back and read the question. It says, "What is the length of each side?" so just writing n=6 is not the correct answer to the question. You have to substitute the value for n (which is 6) into each of the expressions for the sides of the triangle. So the first side was n, which is 6 inches. The second side was 3n+3, which is 3 times 6 + 3, or 18 + 3, which equals 21 inches. The third side was 2n + 11, so 2 times 6 + 11, which is 12 + 11, which equals 23 inches. I would write for my answer: The first side is 6 inches, the second side is 21 inches, and the third side is 23 inches.

You should check your answer to make sure that the sides all add up to 50. So, write the following: 6 + 21 + 23 = 50, and when you add the left side of the equation, you get 50. Since both sides equal 50, you have proven that your answer works and is correct!

I hope that helps! Let me know if you need more help. Word problems take practice, but you can do

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