Question

your bedroom is in the shape of a square that is 14 feet long on each side. will a circular rug with a circumference of 50.24 feet fit in your room? if not, by how many feet is the rug too wide?

Answer 1

The rug is two feet too wide

Explanation:

Well first, let's figure out the diameter of the rug to see if it will fit in the room. We know that the circumference of the circle is πd. So we can solve for d from there (d is the diameter).

c = πd

50.24 = πd

50.24/π = d

d = about 16 ft

Knowing this, we know that the rug would not fit in the room and if it was centered, it would have a foot of rug sticking out from each wall. Therefore, the rug is two feet too wide.

Answer 2

`\huge\boxed{\text{No; 2 feet}}`

We need to find the diameter of the rug and compare it to the side length of the room — which is given.

The formula for the circumference of a circle is below — where
`C` represents the circumference and
`d` represents the diameter.

`C=\pi d`

Plug in the value we know.

`50.24=\pi d`

Replace
`\pi` with its approximate value —
`3.14`.

`50.24=3.14d`

Divide both sides of the equation by
`3.14`.

`16=d`

The diameter of the rug is
`16` feet, which means it will not fit into the room. It is 2 feet too wide (
`16-14`).