Question

Katie wants to hang a painting in a gallery. The painting and frame must have an area of 45 square feet. The painting is 6 feet wide by 7 feet long. Which quadratic equation can be used to determine the thickness of the frame, x?

4x2 + 26x + 45 = 0

4x2 + 26x − 3 = 0

x2 + 13x − 3 = 0

x2 + 13x + 45 = 0

Answer 1

4x² + 26x - 3 = 0

Explanation:

We assume the width of the frame is the same along all sides and is x.

The length of the painting plus the frame is 7 + 2x, or 2x + 7.

The width of the painting plus the frame is 6 + 2x, or 2x + 6.

(2x + 7)(2x + 6) = 45

4x² + 12x + 14x + 42 = 45

4x² + 26x - 3 = 0