SOLUTION: I am tying to find the missing sides of a triangle and leave answers as radicals in simplest form. I have a triangle 45degrees the longer side is 6.

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Question 701526: I am tying to find the missing sides of a triangle and leave answers as radicals in simplest form. I have a triangle 45degrees the longer side is 6.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The sides of a 45-45-90 triangle have ratios +1+ : +1+ : +sqrt%282%29+
You are given the side opposite the 90 angle is +6+
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If you multiply the ratios by a constant, the ratios do not change, so
+k%2A1+ : +k%2A1+ : +k%2Asqrt%282%29+ still describe a 45-45-90 triangle
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What if I say +k+=+6%2Fsqrt%282%29+ ? I then have
+6%2Fsqrt%282%29+ : +6%2Fsqrt%282%29+ : +%28+6%2Fsqrt%282%29+%29%2Asqrt%282%29+ and simplifying:
+6%2Fsqrt%282%29+ : +6%2Fsqrt%282%29+ : +6+
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so, the missing sides are +6%2Fsqrt%282%29+, and simplifying:
+%28+6%2Fsqrt%282%29%29%2A%28+sqrt%282%29+%2F+sqrt%282%29+%29+
+%28+6%2Asqrt%282%29+%29+%2F+2+
+3%2Asqrt%282%29+ answer
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check answer:
+6%5E2+=+%28+3%2Asqrt%282%29+%29%5E2+%2B+%28+3%2Asqrt%282%29+%29%5E2+
+36+=+9%2A2+%2B+9%2A2+
+36+=+18+%2B+18+
+36+=+36+
OK