Final answer:
The mirror will not fit because its total height when hung is greater than the available space on the wall.
Step-by-step explanation:
To determine if the mirror will fit, we need to calculate the length of the mirror. We know that the area of the mirror is 7 9/16 square feet and the width is 2 2/3 feet. To find the length, we divide the area by the width: 7 9/16 ÷ 2 2/3 = 121/16 ÷ 8/3 = (121/16) × (3/8) = 363/128 = 2 107/128 feet. The height of the mirror is given as 3 feet, so we need to add the height to the length to get the total height of the mirror when hung. 3 + 2 107/128 = 3 + (2 × 64 + 107)/128 = 3 + 135/128 = 129/128 feet. Since the height of the space on the wall is 3 feet, the mirror will not fit. Its total height when hung is greater than the available space.