Question

In trapezoid LMNO below, median PQ is drawn.MРooNIf LM = x+7, ON = 3x + 11, and PQ = 25, what isthe value of x?1) 1.75 2) 3.5 3) 8 4) 17

Answer 1

Lenght of median of a trapezoid = (lenght of one base + lenght of other base)/2

In this case, we can write:

PQ = (LM + ON)/2

25 = ((x + 7) + (3x + 11))/2

$25=\frac{(x+7)\text{ + (3x + 11)}}{2}\Longrightarrow\text{ 50 = x + 7 + 3x + 11}$

50 = 4x + 18

4x = 50 - 18

4x = 32

x = 32/8 = 4

x = 4

Answer:

x = 4