SOLUTION: what are the missing side lengths? with answers in reduced radical form http://prntscr.com/ruwwwf

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Question 1155495: what are the missing side lengths? with answers in reduced radical form
http://prntscr.com/ruwwwf
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

your triangle is right triangle with congruent legs because both acute angles are equal
hypothenuse is c=12
legs a=b
using Pythagorean theorem we have:
c%5E2=a%5E2%2Ba%5E2
12%5E2=2a%5E2
144=2a%5E2
a%5E2=144%2F2
a%5E2=72
a=sqrt%2872%29
a=6sqrt%282%29=>b=6sqrt%282%29

Answer by MathTherapy(10557) About Me  (Show Source):
You can put this solution on YOUR website!

what are the missing side lengths? with answers in reduced radical form
http://prntscr.com/ruwwwf 
Hypotenuse of a 45-45-90 right triangle = s√2, with s being the other congruent sides

Hypotenuse of THIS 45-45-90 right triangle = 12 units

We then get: s√2 = 12

s, or each of the 2 congruent sides =