Question

find ef in the trapezoid.
ef = \square

Explanation:

Step1: Apply trapezoid midsegment theorem

The midsegment of a trapezoid is the average of the two bases, so $4x = \frac{(x+3) + 32}{2}$

Step2: Multiply both sides by 2

$8x = x + 3 + 32$

Step3: Simplify right-hand side

$8x = x + 35$

Step4: Isolate x term

$8x - x = 35$
$7x = 35$

Step5: Solve for x

$x = \frac{35}{7} = 5$

Step6: Calculate EF

Substitute $x=5$ into $EF=4x$: $EF = 4\times5$

Answer:

20