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# It's been a while, guys!

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I've actually missed you all!

I've changed a lot- along with my handwriting for that matter- but I've missed you a lot.

I've been trying to get used to 8th grade, but there are a few extra-credit problems I've gotten stuck on.

I can't get credit for them now but I would like to figure it out.

My teacher gave me the teacher's edition, but it had nothing but the answer. I would like to know how to get to the answer itself though.

The problem is:

The lengths of the sides of a triangle are 4n, 2n+10, and 7n-15. Is there a value of n that makes the triangle equilateral? Explain.

Without using brute force, I could not get the answer.

file:///C:/Users/Jimin%20Bang/Desktop/20191026_214359.jpg

Oct 27, 2019
edited by tommarvoloriddle  Oct 27, 2019
edited by tommarvoloriddle  Oct 27, 2019

#1
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The lenghts of an equilateral triangle must be equal so do the angles, so each side opposite to the angle must be 60 degrees (The angle) and so all the sides must be equal to that side.

First let's add all of them and combine like terms:

4n+2n+10+7n-15=60 Why set 60? because the angle infront of each side is 60'degrees.

13n-5=60

solve for n

n=5

Subsituite n=5 in each side of the triangle

4n=4(5)=20

2n+10=2(5)+10=20

7n-15=7(5)-15=20

All sides are equal to 20 so that is an equilateral triangle.

Oct 27, 2019
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Thank you!

Can you tell what is wrong with my work, if you can see it?

file:///C:/Users/Jimin%20Bang/Desktop/20191026_214359.jpg

tommarvoloriddle  Oct 27, 2019
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and welcome back :))

Guest Oct 27, 2019
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These type of files don't open except on your device

Guest Oct 27, 2019
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:)

Thank you so much!

tommarvoloriddle  Oct 27, 2019
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Okay, so how can I make it accessible to you?

tommarvoloriddle  Oct 27, 2019
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Screen shot it and upload it i think

Guest Oct 27, 2019
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unfor. i have to go now :( but i am pretty sure someone will answer you :))

Guest Oct 27, 2019
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Thank you for helping me!

I can't upload it- it says no file selected...

:<

tommarvoloriddle  Oct 27, 2019
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Never mind now!

tommarvoloriddle  Oct 27, 2019
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Never mind it is working!!!

Is there a way to go from here?

Oct 27, 2019
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Solution:

The easiest method to solve this is to set any two of the terms as equal.

$$\text {4n= 2n+10 | (set as equal)}\\ \text {2n=10 | (simplify)}\\ n=5$$

Guest’s solution “4n+2n+10+7n-15=60 Why set 60? because the angle infront of each side is 60'degrees,” is non sequitur. The equations have nothing to do with the angles. If they did, then the sum should be 180. This method is capricious (means bullshit, here) and works because of coincidence.

GA

Oct 27, 2019
edited by GingerAle  Oct 27, 2019
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Yeah, I just set two equal, no need to overthink it.

CalculatorUser  Nov 2, 2019
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Hi Tom...riddle

Oct 27, 2019
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Hi Melody!!!

I've missed you all!

tommarvoloriddle  Oct 27, 2019