Question

Emily wants to hang a painting in a gallery. The painting and frame must have an area of 31 square feet. The painting is 5 feet wide by 6 feet long. Which quadratic equation can be used to determine the thickness of the frame, x?
Image of a frame 5 feet wide by 6 feet long, with an of x on the bottom and right sides.
4x2 + 22x − 1 = 0
4x2 + 22x + 31 = 0
x2 + 11x − 1 = 0
x2 + 11x + 31 = 0

Answer 1

Emily could start with the quadratic equation

... (2x+5)(2x+6)=31

... 4x² +22x +30 = 31

And then subtract the right side to put it into standard form.

... 4x² +22x -1 = 0 . . . . . . corresponds to the first selection

Answer 2

The correct answer is 4x2 + 22x − 1 = 0  

That's what you get when you (5 + 2x)(6 + 2x) = 31

And you get to expand that based on the data that is already provided in the question.