Answer:
EF = 22 , AB = 1
Step-by-step explanation:
the midsegment of a trapezoid is equal to half the sum of the parallel bases
EF = [tex]\frac{1}{2}[/tex] (AB + DC ) ← substitute values
x + 6 = [tex]\frac{1}{2}[/tex] (2x - 9 + x + 5) ← multiply both sides by 2 to clear the fraction
2x + 12 = 3x - 4 ( subtract 3x from both sides )
- x + 12 = - 4 ( subtract 12 from both sides )
- x = - 16 ( multiply both sides by - 1 )
x = 16
Then
EF = x + 6 = 16 + 6 = 22
Similarly
EF = [tex]\frac{1}{2}[/tex] (AB + DC ) , that is
x + 3 = [tex]\frac{1}{2}[/tex] (4x - 3 + 2x + 5 ) ← multiply both sides by 2 to clear the fraction
2x + 6 = 6x + 2 ( subtract 6x from both sides )
- 4x + 6 = 2 ( subtract 6 from both sides )
- 4x = - 4 ( divide both sides by - 4 )
x = 1
Then
AB = 4x - 3 = 4(1) - 3 = 4 - 3 = 1
