Question

David wants to hang a mirror in his room but the mirror and frame must not have an area larger than 8 square feet. The mirror is 2 feet wide and 3 feet long. Which quadratic equation represents the area of the mirror and frame combined?

Answer 1

The equation would be `(2 + 2x)(3 + 2x) = 8`, where `x` represents the width of the frame.

Explanation:

For problems like these, I would strongly recommend you draw a diagram.

Letting the length difference between the length of the frame and the length of the mirror be `x`, we can write the following equation.

`A = (2 + 2x)(3 + 2x)`

However, since the area of the mirror and frame combined cannot exceed `8` square feet, we can write that

`8 ≥ (2 + 2x)(3 + 2x)`

Assuming that David wants the mirror with the largest possible area, we can change the inequality sign to an equal.

`8 = (2 + 2x)(3 + 2x)`

Hopefully this helps!