EXPLANATION:
We are given two triangles which are similar, and they are;
[tex]\Delta DEF\cong\Delta GHI[/tex]
If both triangles are similar, then the corresponding sides will have the ratios as shown;
[tex]\frac{DE}{GH}=\frac{EF}{HI}=\frac{DF}{GI}[/tex]
Now, we are given the following sides;
[tex]\begin{gathered} DE=15,EF=31, \\ GH=59,HI=x \end{gathered}[/tex]
Using the ratios of similar triangles as shown above, we now have;
[tex]\frac{15}{59}=\frac{31}{x}[/tex]
Next we solve for x. We start by cross multiplying;
[tex]x=\frac{31\times59}{15}[/tex][tex]x=\frac{1829}{15}[/tex][tex]x=121.93[/tex]
Rounded to the nearest tenth, the answer is;
ANSWER:
[tex]x=121.9[/tex]
