I'm doing a geo problem and I've come upon this: JL is 6√6 and JK is 24, but JK is the hypotenuse and 6√6 if I'm not mistaken is 216 because 36*6 is 216...is this just a mistake the teacher made or am I missing something?

Question

anonymous · Answer

i'll give a medal to the first person who can answer it correctly!

anonymous · Answer

6*sqrt(6) = 14.7

anonymous · Answer

no no no.  6 radical 6

raden · Answer

do you have a diagram ?

anonymous · Answer

that would be 36 * 6 right?

anonymous · Answer

yeah hold on

anonymous · Answer

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anonymous · Answer

36*6 = 216
6*sqrt(6) = 14.7

i'm not quite sure what you are trying to figure out more...?

anonymous · Answer

look at the diagram

anonymous · Answer

what are you solving for, the remaingit side?

anonymous · Answer

oh and i forgot to add the larger triangle is also right

anonymous · Answer

yes

anonymous · Answer

are there any interiror angle values aside from 90?

anonymous · Answer

hold on, i just want to know, 6 radical 6 is the same as 36*6

anonymous · Answer

nope, not the same
36*6 = 216 
6*sqrt(6) = 14.7

anonymous · Answer

but if simplifying the √ 216, wouldn't it turn out to be 6√ 6?

raden · Answer

yeah, you are right. the simplify of √ 216 is 6√ 6
in other words, if you squres 6√ 6, get 216

anonymous · Answer

thank you that's what i needed to confirm

anonymous · Answer

36*6 = 216 

6*sqrt(6) = 14.7
(6*sqrt(6))^2 = 216

raden · Answer

btw, where the position of point J,K,L ? and what are you solving for ?

anonymous · Answer

|dw:1398119750275:dw|

anonymous · Answer

i'm finding JM LM and LK

anonymous · Answer

i know i have to use pythag theorem, but i just thought it was confusing that the hypotenuse is 24 and the leg is 6√ 6

raden · Answer

oh, okay. good idea by using the pythagorean theoremt easier to find LK. we can use the formula :
LK^2 = JK^2 - JL^2
so,
LK^2 = (24)^2 - (6√ 6)^2
simplify the RHS, then solve for LK ...

anonymous · Answer

thank you

raden · Answer

and actually, to get JM. we can use the similarities of both triangle are JLM and JLK, see the corresponding of side of them then take the proportion :
JL/JK = JM/JL
get
(6√ 6)/24 = JM/(6√ 6)
solve for JM ....

raden · Answer

after you get JM, then see the triangle of JLM (right triangle). again use the pythagorean theorem :
LM^2 = JL^2 - JM^2