Answer:
EF = 75
Step-by-step explanation:
The median of a trapezoid is half the sum of the parallel bases, that is
EF = [tex]\frac{AB+DC}{2}[/tex] ( substitute expressions for lengths of sides )
5x = [tex]\frac{5x+20+3x+10}{2}[/tex]
5x = [tex]\frac{8x+30}{2}[/tex] ( multiply both sides by 2 to clear the fraction )
10x = 8x + 30 ( subtract 8x from both sides )
2x = 30 ( divide both sides by 2 )
x = 15
substitute x = 15 into the expression for EF
EF = 5x = 5 × 15 = 75
