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 quadratic equation can be used to determine the thickness of the frame, x is 4x2 + 22x − 1 = 0.

What is the quadratic equation?

The polynomial equation whose highest degree is two is called a quadratic equation or sometimes just quadratics.

Let x be the thickness of the frame.

The painting and frame must have an area of 31 square feet.

The painting is 5 feet wide by 6 feet long.

The area of the frame is given by;

$\rm Area=length \times width\\\\31= (2x+5)(2x+6)\\\\31 = 2x(2x+6)+5(2x+6)\\\\31= 4x^2+12x+10x+30\\\\31=4x^2+32x+30\\\\4x^2+32x+30-31=0\\\\4x^2+32x-1=0$

Hence, the quadratic equation can be used to determine the thickness of the frame, x is 4x2 + 22x − 1 = 0.

Learn more about quadratic equation here;

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