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## daustin15 AC + BC could equal 15 Always Never Sometimes one year ago one year ago

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1. daustin15

2. UsukiDoll

Well one side is 9. This can get tricky since if A = 1, B = 1, and C = 9 you'll have 18. And you can't have a zero side or a negative side. That's impossible

3. ParthKohli

$\rm AC = 9$Now apply the Pythagorean Theorem.$9^2 + x^2 = 15^2$Any solutions to the above?

4. ParthKohli

Turns out they could never, because the only solution is $$12$$ but $$9 + 12 = 21$$

5. ParthKohli

Also thinking about how AC + BC > 15, we could never get AC + BC = 15.

6. UsukiDoll

oh I remember doing that PArth...

7. ParthKohli

Erm?

8. UsukiDoll

the a^2+b^2 = c^2

9. Directrix

Triangle Inequality Theorem: One side of a triangle is less than the sum of the other two. Therefore, 15 < AC + BC which is equivalent to AC + BC > 15. AC + BC could never be equal to 15. There would be no triangle. @daustin15