Chapter 7.1, Problem 55SPR

To determine

To find: The value of $x$ in the given figure.

Answer to Problem 55SPR

The value of $x$ is $2.5$ .

Explanation of Solution

Given:

The given figure is as follows.

  

Here, $CD=9x$ , $ST=15$ , and $AB=3x$ .

Calculation:

The length of the mid-segment of a trapezoid is half the sum of the lengths of the bases.

Write the equation and solve for $x$ .

  $\begin{array}{c}15=\frac{3x+9x}{2}\\ 15\times 2=12x\\ 30=12x\\ x=\frac{30}{12}\end{array}$

Simplify further.

  $x=2.5$

Therefore, the value of $x$ is $2.5$ .