Question

question 4 of 10 given the median (overline{qr}) and trapezoid (mopn), what is the value of (x)?

Explanation:

Step1: Recall trapezoid - median formula

The formula for the length of the median of a trapezoid is $QR=\frac{OP + MN}{2}$, where $QR$ is the median, $OP$ is the length of the shorter base, and $MN$ is the length of the longer base.

Step2: Substitute the given expressions

We are given that $QR = 27$, $OP=5x - 7$, and $MN = 6x+6$. Substituting into the formula gives $27=\frac{(5x - 7)+(6x + 6)}{2}$.

Step3: Simplify the right - hand side

First, simplify the numerator of the right - hand side: $(5x - 7)+(6x + 6)=5x-7 + 6x+6=11x-1$. So the equation becomes $27=\frac{11x - 1}{2}$.

Step4: Solve for x

Multiply both sides of the equation by 2: $27\times2=11x - 1$, which is $54=11x - 1$. Then add 1 to both sides: $54 + 1=11x$, so $55 = 11x$. Divide both sides by 11: $x = 5$.

Answer:

D. 5