Catarina and Tom want to buy a rug for a room.

Question

Catarina and Tom want to buy a rug for a room that is 12 by 20 feet. They want to leave an even strip of flooring uncovered around the edges of the room. How wide a strip will they have if they buy a rug with an area of 128 square feet?

Answer 1

Our first equation represents the area of the rug with side lengths x and y:

 

x * y = 128 sq. ft.

 

Our second equation will make sure that the strip around the room is uniform in size:

 

12 - x = 20 - y

 

Now, solve for x:

 

x = y - 8

 

Next, substitute this value for x into the first equation and solve for y:

 

128 = (y - 8) * y

128 = y² - 8y

y² - 8y - 128 = 0

(y - 16) * (y + 8)

y = 16, y = -8

 

We can disregard y = -8 as a solution because in this problem, -8 is not meaningful as a "length".

 

So, we now substitute y = 16 back into our first equation and find that x = 8.

 

Thus, these side lengths 8 and 16, create a rug that is 128 square feet and this rug leaves an even 4 foot strip of flooring uncovered around the edges of a 12 by 20 foot room.