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.

Somebody, please help?

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

tommarvoloriddle Oct 27, 2019

#1**+1 **

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.

Guest Oct 27, 2019

#2**+1 **

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

#9**0 **

Thank you for helping me!

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

:<

tommarvoloriddle
Oct 27, 2019

#12**+2 **

Solution:

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

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

Additional comments:

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

GingerAle Oct 27, 2019