Question

Question 17GeometryFind the length of the midsegment of the trapezoid

Answer 1

17) We have to find the length of the midsegment of the trapezoid.

From the picture we can conclude that the midsegment is the average between the side at the top and the side at the bottom.

Then we can write:

`\begin{gathered} n+12=(1)/(2)[(2n-2)+(4n+6)] \\ n+12=(1)/(2)(2n-2+4n+6) \\ n+12=(1)/(2)(6n+4) \\ n+12=3n+2 \\ n-3n=2-12 \\ -2n=-10 \\ n=(10)/(2) \\ n=5 \end{gathered}`

Knowing n = 5, we can find the length of the midsegment as:

`n+12=5+12=17`

Answer: the midsegment has a length of 17 units.