Question

Use the following diagram to solve for x

Answer 1

Since both triangles are similar, the ratio between their sides remains constant. Therefore,

`(6)/(12)=(x+6)/(12+27)`

Solving for x,

`\begin{gathered} (6)/(12)=(x+6)/(12+27)\rightarrow(1)/(2)=(x+6)/(39)\rightarrow(39)/(2)=x+6 \\ \rightarrow x=(39)/(2)-6 \\ \Rightarrow x=13.5 \end{gathered}`

Therefore, x = 13.5