Question

Tabitha wants to hang a painting in a gallery. The painting and frame must have an area of 58 square feet. The painting is 7 feet wide by 8 feet long.

Which quadratic equation can be used to determine the thickness of the frame, x?

(See picture attached below)

Answer Choices:
A. x2 + 15x − 2 = 0
B. x2 + 15x + 58 = 0
C. 4x2 + 30x − 2 = 0
D. 4x2 + 30x + 58 = 0

Answer 1

C

Explanation:

took the test

Answer 2

If the total area of the painting and the frame is 58 sq ft, we have the equation:
(8 + 2x)(7 + 2x) = 58

Expanding the equation,
56 + 30x + 4x^2 = 58

Combining like terms and arranging the equation, we have:
4x^2 + 30x - 2 = 0

Therefore, the answer is
C. 4x2 + 30x − 2 = 0