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?

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Answer 1 · 2016-10-15T14:34:17

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

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

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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!