Question

PLEASE HELP WILL MARK BRAINLIEST

Answer 1

Step-by-step explanation:

In trapezoid ABCD, it is given that:

AE = BE & DF = CF

Hence, points E and F are the mid points of the sides AB and CD respectively.

We know that:

In a trapezoid length of the line segment joining the mid points of non parallel sides is equal to one half of the sum of lengths of the parallel sides.

$\therefore \: 4x = \frac{1}{2} \{(x + 5) + 44 \} \\ \\ \therefore \: 4x = \frac{1}{2} \{x + 5 + 44 \} \\ \\ \therefore \: 4x \times 2= \{x + 49\} \\ \\ \therefore \: 8x = x + 49 \\ \\ \therefore \: 8x - x = 49 \\ \\ \therefore \: 8x - x = 49 \\ \\ \therefore \:7x = 49 \\ \\ \therefore \:x = \frac{49}{7} \\ \\ \therefore \:x = 7\\ \\ \therefore \:4x = 4\times 7.. (\because EF = 4x)\\ \\ \: \: \: \: \: \huge \red{ \boxed{\therefore \:EF = 28}}$