Answer: 63.9
Step-by-step explanation:
ΔEDH ~ ΔEGD
Set a proportion to solve for ED.
Then set up a proportion to solve for x.
[tex]\dfrac{ED}{EH}=\dfrac{EG}{ED}\quad \rightarrow \quad \dfrac{ED}{112}=\dfrac{99.2}{ED}\quad \rightarrow \quad ED^2=112(99.2)\quad \rightarrow \quad ED=105.4\\\\\\\dfrac{DG}{DH}=\dfrac{EG}{ED}\quad \rightarrow \quad \dfrac{62}{x+2}=\dfrac{99.2}{105.4}\quad \rightarrow \quad 62(105.4)=99.2(x+2)\\\\\\62(105.4)=99.2(x+2)\\\\6535.2=99.2(x+2)\qquad \text{simplified left side}\\\\65.9=x+2\qquad \text{divided both sides by 99.2}\\\\63.9=x\qquad \text{subtracted 2 from both sides}[/tex]
