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 $\text{AB}=\mathbf{5}\text{x}$and $\text{BC}=\mathbf{2}\text{x}+\mathbf{12}$ then $\text{x}=$ ? .

Short answer

The length of x is 4 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 AB and BC are $5x$ and$2x+12$ 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 x is calculated as follows:

$\begin{array}{c}AB=BC\\ 5x=2x+12\\ 3x=12\\ x=4\end{array}$

Thus, the length of x is 4 units.

Step 3. State the conclusion.

Therefore, the length of x is 4 units.