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One way we create expressions is by starting with given dimensions.

Example: Andrew wants to build a rectangular holding pen for his sheep. The length of the rectangle is twice as long as the width. He wants to put a fence around the pen, so he needs to calculate its perimeter. Write an expression for the perimeter of this pen.

There are two unknown quantities in this case - the length and the width of the rectangle.
- Call the width of the pen [tex]\( a \)[/tex].
- The expression for the length is [tex]\( 2a \)[/tex].
- Use the formula for the perimeter of a rectangle to express the perimeter of the pen in terms of [tex]\( a \)[/tex].

[tex]\[
\begin{aligned}
\text{Perimeter of rectangle} & = 2(\text{length} + \text{width}) \\
& = 2(2a + a) \\
& = 2(3a) \\
& = 6a
\end{aligned}
\][/tex]



Answer :

GinnyAnswer
Let's address the problem step-by-step.

### Unknown Quantities
There are two unknown quantities in this case—the width and the length of the rectangle.

- Call the width of the pen [tex]\( a \)[/tex].

### Expression for the Length
The problem states that the length of the rectangle is twice as long as the width.

- Therefore, the expression for the length is [tex]\( 2a \)[/tex].

### Formula for the Perimeter of a Rectangle
The formula for the perimeter of a rectangle is given by:

[tex]\[ \text{perimeter of rectangle} = 2 \times (\text{length} + \text{width}) \][/tex]

- Substitute the expressions for the length and width into the formula:

[tex]\[ \begin{aligned} \text{perimeter of rectangle} &= 2 \times (\text{length} + \text{width}) \\ &= 2 \times (2a + a) \\ &= 2 \times (3a) \\ &= 6a \end{aligned} \][/tex]

So, the expression for the perimeter of Andrew's holding pen is [tex]\( 6a \)[/tex].

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