Hello again! So we will be using the pythagorean theorem ([tex]leg^2+leg^2=hypotenuse^2[/tex]) to solve for the bottom leg of the triangles. After we do that, we'll subtract the value of the legs from 31, and that'll be x.
Plug in 17 and z (or any variable that isn't x) into the leg variable and 19 into the hypotenuse variable, and from there we can solve.
[tex]17^2+z^2=19^2[/tex]
Solve the exponents to get [tex]289+z^2=361[/tex]
Subtract 289 on each side to get [tex]z^2=72[/tex]
Lastly, square root each side of the equation and your answer should be [tex]z= \sqrt{72}[/tex] (To get more accurate answers, you shouldn't round until the end of the problem)
Nextly, we will need to subtract [tex] \sqrt{72}[/tex] from 31. And since there are 2 triangles, you'll need to multiply [tex] \sqrt{72}[/tex] by 2.
[tex]x=31- \sqrt{72} *2 \\ x=14.0[/tex]
In short, x = 14.0
