Merriam and Emmanuel assemble a new bookshelf. Its 1ft deep,4ft wide, and 8ft tall. They assemble it flat bit when they tip it up The shelf hits the ceiling. They can cut a little off the legs to make the bookshelf shorter. What is the least amount in inches they can cut off in order to be able to raise the bookshelf?
In order to find the least amount they can cut off the legs to raise the bookshelf, we need to determine the height of the bookshelf once it is standing upright.
The original height of the bookshelf is 8ft, which is equal to 8 * 12 = <<8*12=96>>96 inches.
Now let's consider the height of the ceiling. Since the shelf hits the ceiling when it is upright, the height of the ceiling is the maximum height the bookshelf can have.
In order to find the least amount they can cut off the legs, we need to subtract the height of the ceiling from the original height of the bookshelf:
96 inches - (height of the ceiling) = least amount they can cut off the legs
However, we don't have information about the height of the ceiling, so we cannot determine the exact least amount they can cut off the legs without knowing the height of the ceiling.
To determine the least amount that needs to be cut off the legs of the bookshelf, we need to calculate how much space is available between the top of the bookshelf and the ceiling.
Given that the bookshelf is 8ft tall, we need to convert it to inches since the height of the ceiling will also be in inches.
1 foot = 12 inches
So, the height of the bookshelf is 8 ft * 12 in/ft = 96 inches.
To determine how much space is available between the bookshelf and the ceiling, we need to subtract the height of the bookshelf from the height of the ceiling.
Assuming the height of the ceiling is h inches, the space available is given by:
Space available = h inches - 96 inches
To be able to raise the bookshelf, the space available should be greater than or equal to the depth of the bookshelf, which is 1 foot = 12 inches.
Therefore, we have the inequality:
h inches - 96 inches ≥ 12 inches
Simplifying the inequality, we get:
h inches ≥ 108 inches
To find the least amount that needs to be cut off from the legs, we take the minimum value of h that satisfies the inequality.
Therefore, the least amount they can cut off the legs is 108 inches.
To determine the least amount in inches that Merriam and Emmanuel can cut off from the legs of the bookshelf in order to raise it, we first need to calculate how much clearance they require between the bookshelf and the ceiling.
Given that the bookshelf is 1ft (12 inches) deep, 4ft (48 inches) wide, and 8ft (96 inches) tall, the width and depth of the bookshelf will not affect its ability to fit in the room without modification.
However, the height of 8ft (96 inches) is what is causing the bookshelf to hit the ceiling when it is tipped up.
To find the required clearance, subtract the height of the bookshelf from the height of the ceiling. Assuming the ceiling height is not specified, let's solve this problem by setting an example ceiling height of 9ft (108 inches).
Ceiling height - Bookshelf height = Clearance
108 inches - 96 inches = 12 inches
In this scenario, they would need a clearance of 12 inches between the bookshelf and the ceiling in order to raise it without it hitting the ceiling.
Therefore, the least amount in inches they can cut off from the legs of the bookshelf to be able to raise it is 12 inches.