SOLUTION: find the length x in the following triangle express it in simplified radical form the left side is 12 the right side is x and the bottom is 8

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: find the length x in the following triangle express it in simplified radical form the left side is 12 the right side is x and the bottom is 8      Log On


   

Question 88049: find the length x in the following triangle
express it in simplified radical form
the left side is 12 the right side is x and the bottom is 8
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Since we have a triangle with legs of 8 , x(our unknown side) and a hypotenuse of 12, we can use Pythagoreans theorem to find the unknown side.
Pythagoreans theorem
a%5E2%2Bb%5E2=c%5E2

8%5E2%2Bx%5E2=12%5E2 Plug in a=8, b=x and c=12 and lets solve for x
6+4+%2B++x++%5E+2+=+1+4+4 Square each individual term



+x++%5E+2+=+1+4+4+-+6+4 Subtract 64 from both sides


+x++%5E+2+=+8+0 Combine like terms


s+q+r+t+%28++x++%5E+2+%29+=+s+q+r+t+%28+8+0+%29 Take the square root of both sides


x=4%2Asqrt%285%29 Simplify the square root


Which approximates to...
x+=+8+.+9+4+4+2+7+1+9+0+9+9+9+9+1+6

So our answer is
x+=+8+.+9+4+4+2+7+1+9+0+9+9+9+9+1+6