Question

Triangle HFG is similar to triangle RPQ. Find the value of x. Find the length of HG.

Answer 1

• x=1

,

• HG=8 units

Step-by-step explanation:

If triangles HFG and RPQ are similar, the ratios of their corresponding sides are:

`(HF)/(RP)=(HG)/(RQ)=(FG)/(PQ)`

Substitute the given values:

`(4)/(2)=(6x+2)/(x+3)=(6)/(3)`

First, we solve for x:

`\begin{gathered} (4)/(2)=(6x+2)/(x+3) \\ 2=(6x+2)/(x+3) \\ 2(x+3)=6x+2 \\ 2x+6=6x+2 \\ 6-2=6x-2x \\ 4=4x \\ x=1 \end{gathered}`

Finally, calculate the length of HG.

`\begin{gathered} HG=6x+2 \\ =6(1)+2 \\ =8\text{ units} \end{gathered}`