Question

David wants to hang a mirror in his room. The mirror and frame must have an area of 8 square feet. The mirror is 2 feet wide and 3 feet long. Which quadratic equation can be used to determine the thickness of the frame, x?
2x2 + 14x − 2 = 0
3x2 + 10x − 8 = 0
4x2 + 10x − 2 = 0
x2 + 7x − 8 = 0

Answer 1

The correct quadratic equation;
x2+7x-2=0

Working
Assuming the frame has a uniform thickness;
Then length of mirror and frame is 3+x and width 2+x

The area of mirror and frame area;
A=L*W
8=(3+x)(2+x)
8=(6+5x+x2)
Taking 8 to the Right hand side, we have:
x2+5x-2 =0 

Answer 2

Represent the thickness of the frame by x. Framing the mirror will increase both its length and width by 2x. The area of the mirror with the frame is the product of the length and width which can mathematically be expressed as,                                 

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

The equation above can be simplified into 4x^2 + 10x -2 = 0. This equation can still be further simplified by dividing it by 2. However, it will give an answer which is not found on the choices. Thus, the answer is the third choice.