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The length of a rectangle is [tex]$x$[/tex] feet. Its width is [tex]$(x-7)$[/tex] feet.

Draw and label a rectangle to represent this situation. Then write three different expressions you could use to find its perimeter.

Show your work.

Sagot :

GinnyAnsweridn
Certainly! Let's work through this step-by-step.

### Step 1: Draw and Label a Rectangle

First, let's draw a rectangle.

```
x (Length)
+-----------+
| |
| | Width: (x - 7)
| |
+-----------+
```

Here, the length of the rectangle is labeled as [tex]\( x \)[/tex] feet and the width is [tex]\( x - 7 \)[/tex] feet.

### Step 2: Write Three Different Expressions for the Perimeter

The perimeter [tex]\( P \)[/tex] of a rectangle can be found using the formula:
[tex]\[ P = 2 \times (\text{Length} + \text{Width}) \][/tex]

#### Expression 1: Using the Perimeter Formula Directly
[tex]\[ P_1 = 2 \times (x + (x - 7)) \][/tex]
[tex]\[ P_1 = 2 \times (2x - 7) \][/tex]
[tex]\[ P_1 = 4x - 14 \][/tex]

#### Expression 2: Summing Up all Sides Separately
The perimeter is also the sum of all the sides.
[tex]\[ P_2 = x + (x - 7) + x + (x - 7) \][/tex]
[tex]\[ P_2 = 4x - 14 \][/tex]

#### Expression 3: Using an Alternative Form of the Perimeter Formula
Another way to think about the perimeter is the sum of two lengths and two widths.
[tex]\[ P_3 = 2x + 2(x - 7) \][/tex]
[tex]\[ P_3 = 2x + 2x - 14 \][/tex]
[tex]\[ P_3 = 4x - 14 \][/tex]

### Final Simplified Expressions

So, the three different expressions for the perimeter of the rectangle are:
[tex]\[ P_1 = 4x - 14 \][/tex]
[tex]\[ P_2 = 4x - 14 \][/tex]
[tex]\[ P_3 = 4x - 14 \][/tex]

Thus, regardless of the method used, the perimeter of the rectangle simplifies to [tex]\( 4x - 14 \)[/tex] feet.
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