Question

Find the value of x. Round your answer to the nearest tenth.

Answer 1

Hello again! So we will be using the pythagorean theorem ($leg^2+leg^2=hypotenuse^2$) 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.

$17^2+z^2=19^2$

Solve the exponents to get $289+z^2=361$

Subtract 289 on each side to get $z^2=72$

Lastly, square root each side of the equation and your answer should be $z= \sqrt{72}$ (To get more accurate answers, you shouldn't round until the end of the problem)


Nextly, we will need to subtract $\sqrt{72}$ from 31. And since there are 2 triangles, you'll need to multiply $\sqrt{72}$ by 2.

$x=31- \sqrt{72} *2 \\ x=14.0$

In short, x = 14.0