Question

Solve for x. Enter as a decimal not as a fraction. Round to nearest hundredth (2 decimals) if necessary.

Answer 1

We know that the midsegment connects the midpoints because it divides each side into equal parts.

We also know that x+2 and 6x+1 are parallels because the midsegment connects midpoints, which means it's parallel to the third side.

Let's call one side 2y and each part as y. We can use the following proportion

`(y)/(x+2)=(2y)/(6x+1)`

Now, we solve for x.

`\begin{gathered} y(6x+1)=2y(x+2) \\ 6x+1=(2y(x+2))/(y) \\ 6x+1=2(x+2) \\ 6x+1=2x+4 \\ 6x-2x=4-1 \\ 4x=3 \\ x=(3)/(4)=0.75 \end{gathered}`

Hence, x = 0.75.