Answer:
[tex]x=\frac{180}{13}=13.85[/tex]Step by step explanation:
We can solve this situation by using proportions for similar right triangles:
[tex]\frac{\text{shorter leg in EGF}}{\text{shorter leg in EHG}}=\frac{\text{hypotenuse in EGF}}{\text{hypotenuse in EHG}}[/tex]Substitute and solve for x:
[tex]\begin{gathered} \frac{15}{x}=\frac{39}{36} \\ 36\cdot15=39x \\ 540=39x \\ x=\frac{540}{39} \\ x=\frac{180}{13}=13.85 \end{gathered}[/tex]