Answer:
6√3
Explanation:
Let's take the vertical side in the middle as y and the side on the left as z.
We have:
from the right triangle on the right:
9²+y²=x²
from the right triangle over the big triangle:
z²+x²=(9+3)²=12²
from the right triangle on the left:
3²+y²=z²
We can use substitution in our three equations to get x.
9²+y²=x²
z²+x²=12²
3²+y²=z²
First, solve for y² in terms of x². We want everything in terms of x so we can solve for it.
9²+y²=x²
subtract 9² from both sides
x²-81 = y²
plug that into the third equation
3²+(x²-81)=z²
x²-72=z²
z²+x²=144 (the second equation)
plug x²-72 for z²
x²-72+x² = 144
add 72 to both sides
2x² =216
divide both sides by 2 to isolate x²
x²=108
square root both sides to get x
x = √108 = 6√3