Question

If RT = 36, RS = 2x + 3 and ST = 7x + 6, find RSand ST.

Answer 1

We know that RT=36 and that RS=2x+3 and ST=7x+6. We notice that

`RT=RS+ST`

Then, plugging the corresponding values and expressions we have

`36=(2x+3)+(7x+6)`

Solving this equation for x,

`\begin{gathered} 36=(2x+3)+(7x+6) \\ 36=2x+3+7x+6 \\ 36=9x+9 \\ 36-9=9x \\ 27=9x \\ x=(27)/(9) \\ x=3 \end{gathered}`

Then te value of x is 3.

Once we have the value of x we are able to find the value of RS and ST, we just have to substitute said value in the expressions. Then

`\begin{gathered} RS=2(3)+3=6+3=9 \\ ST=7(3)+6=21+6=27 \end{gathered}`

Therefore RS=9 and ST=27.