Question

The high school athletics department is installing a new rectangular addition to their current practice field. the length of the new addition will be at least 10 meters more than twice the width of the new addition. the original field has an area of 300 square meters. the area of the entire practice field, with the addition, must be no more than 1,200 square meters. if a represents the area of the entire practice field, including the new addition, and x represents the width of the new addition, in meters, which system of inequalities can be used to represent this situation?

Answer 1

The system of inequalities that best describes this situation provided A represents the area in which the entire field exists:

$\left \{ {{A \geq x^{2} +10x+300} \atop {A \leq 1200}} \right.$

What are word problems?

Word problems in mathematics exist methods we can utilize variables, algebra notations, and arithmetic operations to solve real-life cases.

We have a new addition to the current rectangular field,

Let that new addition to the current rectangular field be x

Length of the new addition = 10x

Twice the width of the new addition = 2x²

Original area of the field = 300

From the above information, we can derive a quadratic equation:

2x² + 10x + 300

Also, we exist given a constraint that the total area of the practice field should be no more than 1200.

It can be less than 1200 or equivalent to 1200.

Therefore, the system of inequalities that best describes this situation provided A represents the area in which the entire field exists:

$\left \{ {{A \geq x^{2} +10x+300} \atop {A \leq 1200}} \right.$

To learn more about quadratic equations refer to:

https://brainly.com/question/1214333

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