x=18.7
Explanation
Step 1
find the length y ( base of the triangle)
we can set an equation
[tex]\begin{gathered} y+26+y=40 \\ \text{add like terms} \\ 26+2y=40 \\ \text{subtrac 26 in both sides} \\ 26+2y-26=40-26 \\ 2y=14 \\ \text{divide both sides by 2} \\ \frac{2y}{2}=\frac{14}{2} \\ y=7 \end{gathered}[/tex]
so, we have this triangle
Step 2
solve for x, to find x we can apply the Pythagorean theorem it states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse
so
[tex]\begin{gathered} x^2+7^2=20^2 \\ x^2+49=400 \\ \text{subtract 49 in both sides} \\ x^2+49-49=400-49 \\ x^2=351 \\ \text{square root in both sides} \\ \sqrt{x^2}=\sqrt{351} \\ x=18.7349 \\ \text{rounded} \\ x=18.7 \end{gathered}[/tex]
therefore, the answer is
x=18.7
