Answer:
• x=1
,
• HG=8 units
Explanation:
If triangles HFG and RPQ are similar, the ratios of their corresponding sides are:
[tex]\frac{HF}{RP}=\frac{HG}{RQ}=\frac{FG}{PQ}[/tex]
Substitute the given values:
[tex]\frac{4}{2}=\frac{6x+2}{x+3}=\frac{6}{3}[/tex]
First, we solve for x:
[tex]\begin{gathered} \frac{4}{2}=\frac{6x+2}{x+3} \\ 2=\frac{6x+2}{x+3} \\ 2(x+3)=6x+2 \\ 2x+6=6x+2 \\ 6-2=6x-2x \\ 4=4x \\ x=1 \end{gathered}[/tex]
Finally, calculate the length of HG.
[tex]\begin{gathered} HG=6x+2 \\ =6(1)+2 \\ =8\text{ units} \end{gathered}[/tex]
