Question

$\overleftrightarrow{\text{AE}},\overleftrightarrow{\text{BF}},\overleftrightarrow{\text{CG}}$and $\overleftrightarrow{\text{DH}}$are parallel, with $\text{EF}=\text{FG}=\text{GH}$. Complete.

If $\text{AC}=\mathbf{22}-\text{x}$ and $\text{BD}=\mathbf{3}\text{x}-\mathbf{22}$ then $\text{x}=$ ? .

Short answer

The length of x is 11 units.

Step-by-step solution

Step 1. Consider the diagram.

The parallel lines are shown as:

AE, BF, CG and DH are parallel to each other and $EF=FG=GH$. Length of AC and BD are $22-x$ and$3x-22$ respectively.

Step 2. Show the calculation.

Here, ADHE is the trapezoid as AE is parallel to DH.

As $EF=FG=GH$ and AE, BF, CG and DH are parallel to each other, then, the lines BF and CG are the midsegment of the trapezoid.

Hence,

$AB=BC=CD$

The length of AC is:

$\begin{array}{c}AC=AB+BC\\ =BC+BC\end{array}$

Then,

$AC=2BC$ …… (1)

The length of BD is:

$\begin{array}{c}BD=BC+CD\\ =BC+BC\end{array}$

Then,

$BD=2BC$ …… (2)

From equations (1) and (2), the length AC is equal to BD.

The length of x is calculated as follows:

$\begin{array}{c}AB=BD\\ 22-x=3x-22\\ 4x=44\\ x=11\end{array}$

Thus, the length of x is 11 units.

Step 3. State the conclusion.

Therefore, the length of x is 11 units.