# 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?

Oct 15, 2016

The equation would be $\left(2 + 2 x\right) \left(3 + 2 x\right) = 8$, 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.

$A = \left(2 + 2 x\right) \left(3 + 2 x\right)$

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.

$8 = \left(2 + 2 x\right) \left(3 + 2 x\right)$

Hopefully this helps!