Math Destroyer problem

[bjamm]

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hey guys!

2016, Test 11 #12
"Find the radius of the circle inscribed within an equilateral triangle whose side is of length 12"
Answer: 2root3
Can someone please explain the solution for me? i've read it about 1o times already and I still don't know how they got this answer.


Thank you!!!

 

[DOC YANKEM]

hey guys!

2016, Test 11 #12
"Find the radius of the circle inscribed within an equilateral triangle whose side is of length 12"
Answer: 2root3
Can someone please explain the solution for me? i've read it about 1o times already and I still don't know how they got this answer.


Thank you!!!

I can't upload a picture of my work. Give me 10 minutes to create my work on paint. LOL

 

[DOC YANKEM]

Pythagorean Theorem:

(6√3-r)^2 = r^2 + 6^2
(6√3)^2 - 2(6√3 * r) + r^2) = r^2 + 6^2
108 - 12√3r + r^2) = r^2 + 36
72 = 12√3r
6=√3r
r = 6/√3 = 2√3

 

[bjamm]

Pythagorean Theorem:

(6√3-r)^2 = r^2 + 6^2
(6√3)^2 - 2(6√3 * r) + r^2) = r^2 + 6^2
108 - 12√3r + r^2) = r^2 + 36
72 = 12√3r
6=√3r
r = 6/√3 = 2√3

Makes lots of sense now!! thank you so much!