Question

find ef in the trapezoid. ef =

Explanation:

Step1: Recall mid - segment formula

The length of the mid - segment of a trapezoid (EF) is given by $EF=\frac{AD + BC}{2}$, where AD is the length of the top base and BC is the length of the bottom base.

Step2: Set up the equation

We know that $AD = 6$, $EF=4x + 8$, and $BC=9x + 4$. So, $4x + 8=\frac{6+(9x + 4)}{2}$.

Step3: Simplify the right - hand side

First, simplify the numerator of the right - hand side: $6+(9x + 4)=9x+10$. Then the equation becomes $4x + 8=\frac{9x + 10}{2}$.

Step4: Cross - multiply

Multiply both sides of the equation by 2: $2(4x + 8)=9x + 10$.

Step5: Expand the left - hand side

$8x+16 = 9x + 10$.

Step6: Solve for x

Subtract 8x from both sides: $16=x + 10$. Then subtract 10 from both sides to get $x = 6$.

Step7: Find the length of EF

Substitute $x = 6$ into the expression for EF: $EF=4x+8=4\times6 + 8=24 + 8=32$.

Answer:

32