Answer: The width is x + 4
Step-by-step explanation
• The area (,A,) is:
![A=x^2+11x+28](https://img.qammunity.org/2023/formulas/mathematics/college/slxtvn5sucoa29zsj5luwhniqlubggp56z.png)
• The length (,l,) is:
![l=x+7](https://img.qammunity.org/2023/formulas/mathematics/college/gn4etj01tz364ruilo71814xctatwf0jkz.png)
The formula for the area of a rectangle is:
![A=l* w](https://img.qammunity.org/2023/formulas/mathematics/college/lmmzpu3pbc5f31ild3jzkycy7t9l4cj8y8.png)
where w represents the width.
Then, to get the width we have to isolate it in the formula:
![w=(A)/(l)](https://img.qammunity.org/2023/formulas/mathematics/high-school/m5cc4a4lzfonqnan12vctqfnvkvs7ff92y.png)
Replacing the expressions given:
![w=(x^2+11x+28)/(x+7)](https://img.qammunity.org/2023/formulas/mathematics/college/z21jt8x42cujzjofvgekfxos5svie4ahe8.png)
To simplify this expression we can factor the numerator by finding two numbers that when added equal 11, and when multiplied equal 28. For example, 4 and 7:
![4+7=11](https://img.qammunity.org/2023/formulas/mathematics/college/3mls2kfgcdlkqrcr28mswfcyrz404buuyg.png)
![4*7=28](https://img.qammunity.org/2023/formulas/mathematics/college/9hdq50o8szf8klxre4po1woajz5ubz492f.png)
Then, the expression is:
![w=(\left(x+4\right)\left(x+7\right))/(x+7)](https://img.qammunity.org/2023/formulas/mathematics/college/cyucrsbrcruh3u0ci4en986cel0b7hua82.png)
Simplifying:
![w=(x+4)((x+7))/(x+7)](https://img.qammunity.org/2023/formulas/mathematics/college/j21psgb4vrb1btqyfm1r56yya4ssrkfjoa.png)
![w=(x+4)*1](https://img.qammunity.org/2023/formulas/mathematics/college/598bjk0staev75jhxo5ez6e5r5jgw1lsse.png)
Then the width is x + 4.