Question

What is the value of x and what is the length of segment RU?

Answer 1

To find the value of x:

Since, by using RHS congruence rule,

`\Delta\text{RTU}\cong\Delta RTS`

Therefore,

`\begin{gathered} RU=RS \\ 6x+5=8x \\ 5=2x \\ x=2.5 \end{gathered}`

Hence, the value of x is 2.5.

Next, to find the length of line segment RU.

`\begin{gathered} RU=6x+5 \\ =6(2.5)+5 \\ =15+5 \\ =20 \end{gathered}`

Hence, the length of RU is 20.