We can start by finding the area of just the mirror, which is 3 feet x 5 feet = 15 square feet. We know that the total area of the mirror and frame is 19.25 square feet, so the area of just the frame must be 19.25 - 15 = 4.25 square feet.
Let's call the width of the frame "x". Since the mirror is 3 feet wide, the total width of the mirror and frame will be 3 + 2x (one extra x on each side). Since the mirror is 5 feet long, the total length of the mirror and frame will be 5 + 2x. Therefore, the area of the mirror and frame can be expressed as:
(3 + 2x)(5 + 2x) = 19.25
Expanding this equation gives:
15 + 13x + 4x^2 = 19.25
Subtracting 19.25 from both sides gives:
4x^2 + 13x - 4.25 = 0
Therefore, the correct quadratic equation to determine the thickness of the frame, x, is:
4x^2 + 13x - 4.25 = 0
Alexei wants to hang a mirror in his boat and put a frame around it. The mirror and frame must have an area of 19.25 square feet. The mirror is 3 feet wide and 5 feet long. Which quadratic equation can be used to determine the thickness of the frame, x?
2x2 + 8x − 19.25 = 0
3x2 + 5x − 19.25 = 0
4x2 + 16x − 4.25 = 0
4x2 + 16x + 15 = 0
1 answer