Question

Points A, B, E and F are midpoints of $\overline{XC},\overline{XD},\overline{YC}$and $\overline{YD}$. Complete.

If $\text{CD}=\mathbf{8}\text{x}$, and$\text{AB}=\mathbf{3}\text{x}+\mathbf{2}$ then $\text{x}=$ ? .

Short answer

$\text{x}=\mathbf{2}$

Step-by-step solution

Step 1. Consider the diagram.

Here, A, B, E and F are the midpoints of sides $\overline{XC},\overline{XD},\overline{YC}$and $\overline{YD}$respectively.

And $CD=8x$and $AB=3x+2$.

Step 2. Show the calculation.

Consider the triangle $△XCD$.

Here, points A and B are the midpoints of $\overline{XC}$and $\overline{XD}$.

So, by theorem 5-11 part (2), the side $\overline{AB}$is half as long as the third side $\overline{CD}$.

$AB=\frac{1}{2}CD$ …… (1)

Substitute $CD=8x$and $AB=3x+2$.

$\begin{array}{c}AB=\frac{1}{2}CD\\ 3x+2=\frac{1}{2}\left(8x\right)\\ 3x+2=4x\\ 2=4x-3x\\ 2=x\end{array}$

Step 3. State the conclusion.

Therefore, $x=2$.