Solve for x. Each figure is a trapezoid with the median included.

Question

left top Corner (U)
left Middle (B)
left bottom Corner(T)
right top Corner(V)
right Middle (C)
right Bottom corner(W)
top middle (11)
bottom middle (17)
center(4x-30)

Question 6 options:

4

11

9

6

Answer 1

To solve for \( x \) in the context of the trapezoid described, we can use the property of the median (also known as the midsegment) of a trapezoid. The median of a trapezoid is calculated by taking the average of the lengths of the two parallel sides.

In your case:

• The lengths of the parallel sides are given as 11 and 17.
• The median is given as \( 4x - 30 \).

Using the formula for the median of a trapezoid, we have:

\[ \text{Median} = \frac{\text{Length of top side} + \text{Length of bottom side}}{2} \]

This translates to:

\[ 4x - 30 = \frac{11 + 17}{2} \]

Calculating the right-hand side, we get:

\[ 4x - 30 = \frac{28}{2} \] \[ 4x - 30 = 14 \]

Now, we need to solve for \( x \). First, we can add 30 to both sides:

\[ 4x = 14 + 30 \] \[ 4x = 44 \]

Next, divide both sides by 4:

\[ x = \frac{44}{4} \] \[ x = 11 \]

Thus, the value of \( x \) is \( 11 \).

Looking at the options provided:

• 4
• 11
• 9
• 6

The correct answer is \( \boxed{11} \).