Question

find ef in the trapezoid.
ef = \boxed{}

Explanation:

Step1: Apply trapezoid midsegment theorem

The midsegment (EF) of a trapezoid is the average of the two bases (AD and BC).
$$3x+8 = \frac{6 + (7x+3)}{2}$$

Step2: Simplify right-hand side

Combine like terms in the numerator.
$$3x+8 = \frac{7x+9}{2}$$

Step3: Eliminate denominator

Multiply both sides by 2.
$$2(3x+8) = 7x+9$$
$$6x+16 = 7x+9$$

Step4: Solve for x

Isolate x by subtracting $6x$ and 9.
$$16-9 = 7x-6x$$
$$x=7$$

Step5: Calculate EF

Substitute $x=7$ into $3x+8$.
$$EF=3(7)+8=21+8$$

Answer:

29