Question

LM is the midsegment of trapezoid ABCD. AB= x + 8, LM = 4x + 3, and DC = 243. What is the value of x?

Answer 1

x=35

Explanation:

Given ia a trapezoid ABCD with bases AB and CD

Mid segment is LM

AB=x+8

CD =243

LM = mid segment = average of two bases

Hence

LM =
`(x+8+243)/(2) =(x+251)/(2)`

Equate this to given LM value

`(x+251)/(2) =4x+3\\x+251=8x+6\\7x=245\\x=35`

Hence answer is

x=35