Question

given the median qr and trapezoid mnop, what is the value of x? n x + 8 o q 24 r m 5x + 4 p a. 6 b. 18 c. 2 d. 5 e. 7 f. cannot be determined

Explanation:

Step1: Recall median formula for trapezoid

The formula for the length of the median of a trapezoid is $m=\frac{b_1 + b_2}{2}$, where $m$ is the median, $b_1$ and $b_2$ are the lengths of the bases. Here, $m = 24$, $b_1=x + 8$ and $b_2=5x + 4$. So, $24=\frac{(x + 8)+(5x + 4)}{2}$.

Step2: Simplify the right - hand side

First, simplify the numerator of the right - hand side: $(x + 8)+(5x + 4)=x+5x + 8 + 4=6x+12$. Then the equation becomes $24=\frac{6x + 12}{2}$.

Step3: Solve the equation

Multiply both sides of the equation by 2: $24\times2=6x + 12$, which gives $48=6x + 12$. Subtract 12 from both sides: $48-12=6x$, so $36 = 6x$. Divide both sides by 6: $x=\frac{36}{6}=6$.

Answer:

A. 6