Question

Make a sketch and write a quadratic equation to model the situation. Then solve the equation. In art class you are designing the floor plan of a house. The kitchen is supposed to have 150 square feet of space. What should the dimensions of the kitchen be if you want it to be square?

Short answer

The side length of the kitchen needs to be approximately 12.25 feet.

Step-by-step solution

Formulate the equation

The area of a square is given by the formula \(Area = side^2\). Given that the area of the kitchen is 150 square feet, we can write this formula to represent the kitchen: \(side^2 = 150\). This is the quadratic equation that we need to solve.

Solve the quadratic equation

To solve the equation \(side^2 = 150\), we can square root both sides of the equation. The square root of 150 is approximately 12.25. Therefore, \(side = \sqrt{150} \approx 12.25\) feet.

Verify the solution

To verify the solution, we substitute \(side = 12.25\) into the original equation. So, \(side^2 = (12.25)^2 = 150\) square feet. This confirms that the side length solution is correct.