Question

A square carpet covers 75% of the area of the floor.The floor is 8 meters by 8 meters. (a) What are the dimensions of the carpet? (b) What area of the floor is not covered by carpet?

Answer 1

Answer:

The dimensions of the carpet are 4√3m by 4√3m.

16m² are not covered by the carpet.

Step-by-step explanation:

The area of an 8m by 8m floor is 64m².

$8*8=64$

A)

First, 75% of that area is 48m².

$64*0.75=48$

Now we need to find the dimensions of the square carpet. Because it is a square, the length and width have to be the same.

$x*x=48\\x^2=48\\x=\sqrt{48}$

There's 2 ways to simplify that further as it is not a perfect square. Either just use a calculator to find the root, or factor it out. I won't show how to factor that here as it's not directly relevant, but I can explain it if you're interested.

The 2 solutions are:

$x=6.9282...\\x=4\sqrt{3}$

The dimensions of the carpet are 4√3m by 4√3m.

B)

Now to find the area that is not covered, just subtract the area that is covered from the total.

$64-48=16$

16m² are not covered by the carpet.