Question

A floor is 14 feet longer than it is wide. The area of the floor is 1,887 square feet. (a) Write a quadratic equation for the area of the floor (in square feet ) in terms of w, the width in feet.

Answer 1

The quadratic equation for the area (A) of the floor in terms of the width (w) is A = w² + 14w - 1887.

Step-by-step explanation:

Let's denote the width of the floor as "w." According to the given information, the length of the floor is 14 feet longer than its width, so the length would be (w + 14). The area (A) of the floor is given by the product of its length and width: A = w * (w + 14).

Now, set up the quadratic equation:

A = w(w + 14)

Given that the area is 1,887 square feet, we can set up the equation:

w(w + 14) = 1887

Expand and simplify the equation:

w² + 14w - 1887 = 0

Therefore, the quadratic equation for the area of the floor in terms of the width is A = w² + 14w - 1887.

This equation allows us to find the width (w) of the floor by solving for w. The solutions to this quadratic equation will provide the possible values for the width of the floor. The positive solution is the width, and adding 14 to it will give us the length.