Question

Your bedroom is in the shape of a square that is 12 feet long on each side. Will a circular rug with a circumference of 40.82 feet fit into your room? if not, by how many feet is the rug too wide?

Answer 1

We know the area of the rug must be smaller than the area of the room, aye?
we simply need to find the area of the room and the rug, and then compare them :)

the room is easy, we know its a SQUARE, the area for a square is:
l x w = A

the length and width of a SQUARE are always the same
(12 x 12 = 144)

the area of the room is 144 (remember that, we will come back to it later)

now, the area of the CIRCLE
is $A= \pi r^2$
 we are given the circumfrence..... awww dang Dx ughhh okok fine, we can work through this (-~-)

the circumfrence is the distance around a circle (like a perimeter)

$C= \pi (d)$

we know pi is 3.14, we know the circumfrence is 40.82, 

40.82 = 3.14(d)

we now must solve for d by dividing both sides of the equation by 3.14
we get 
d = 13 

YAYYYYY ok, NOW we can find the area of the circle :)

as i was saying, the area is 
A = π r²
where r is the radius (which is Half of the diameter we found earlier)

plugging in the things we know, 

A = (3.14) (13/2)²
 we get
A = 132.665

In conclusion, the area of the circle is less than the area of the square, HOWEVER!!!
 remember how the diameter (of the rug) is 13? The length of the room is only 12 units ;) sneaky little question hahaha, anyways, the rug will NOT fit becuase it has a larger diameter than the rooms length :/

imagine fitting a circle into a square thats too small, the corners fit, but the middles dont :(