Question

Line LM is the midsegment of trapezoid ABCD. AB = x + 8, LM = 4x + 3, and DC = 187. What is the value of x? (image attached)thank you ! :)

Answer 1

To solve that question we must remember that

Then

`\text{ LM = }\frac{\text{ AB + DC}}{2}`

Using the value the problem gives, we get the following equation

`4x+3=((x+8)+187)/(2)`

Solving that equation for x

`\begin{gathered} 4x+3=((x+8)+187)/(2) \\ \\ 8x+6=(x+8)+187 \\ \\ 7x=2+187 \\ \\ 7x=189 \\ \\ x=(189)/(7) \\ \\ x=27 \end{gathered}`

The value of x is 27.