Answer: YES
Step-by-step explanation:
Hi, to answer this question we have to analyze the information given:
- Area of each stain=less than π/100 square feet
- Each one 3 feet from the nearest wall
- Area of rug: 9π square feet
- The centers of the stains are less than 4 feet apart.
First, we have to apply the formula AREA OF A CIRCLE(A)= π r², to obtain the radius of each stain:
π/100 = π r²
π/100 (1/ π)= π r²
1/100 = r²
√1/100 =r
r = 1/10 ⇒ radius of each stain
The centers of the stains are less than 4 feet apart, so:
Max diameter needed to cover is 4+ 1/10 + 1/10 = 21/5 = 4.2
Finally, we have to obtain the diameter of the rug to compare:
Area of rug: 9π
: 9π = π r2 ⇒ r= 3
⇒ d (diameter)= 3 x2 = 6
ft
With statements (1) and (2), we know that the diameter of the rug (6ft) can completely cover both stains (max distance is 4 .2ft)
