Question

In the diagram of \bigtriangleup△GKJ below, LH KJ, GL=6, LK=30, and GH=3. What is the length of GJ?

Answer 1

From the given figures

Since LH // KJ, then

`(GL)/(LK)=(GH)/(HJ)`

GL = 6, LK = 30

GH = 3, HJ = y

Substitute them in the ratio above

`(6)/(30)=(3)/(y)`

By using cross multiplication

`\begin{gathered} 6* y=30*3 \\ 6y=90 \end{gathered}`

Divide both sides by 6

`\begin{gathered} (6y)/(6)=(90)/(6) \\ y=15 \end{gathered}`

Since GJ = GH + HJ

`\begin{gathered} GJ=3+15 \\ GJ=18 \end{gathered}`

The answer is 36