Answer:
[tex]\sqrt19[/tex]
Step-by-step explanation:
First we solve for the biggest triangle: using the Pythagorean theorem, (a^2 + b^2 = c^2) we put in the sides,
9^2 + b^2 = 10^2.
solve, 81 + b^2 = 100
then we subtract 81 from both sides. b^2 = 19, and the answer is [tex]\sqrt 19[/tex].
Now we know what the third side is, which is the hypotenuse for the smaller triangle, so we use the Pythagorean theorem again.
4^2 + x^2 = 19.
Solve
16 + x^2 = 19
Subtract 16 from both sides
x^2 = 19
and finally, we take the square root of both sides
x = [tex]\sqrt19[/tex]
