Question

Please help! will give 14 points and brainliest!

Answer 1

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 = $\frac{1}{2}$ (AB + DC ) ← substitute values

x + 6 = $\frac{1}{2}$ (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 = $\frac{1}{2}$ (AB + DC ) , that is

x + 3 = $\frac{1}{2}$ (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