Respuesta :
Answer:
The first rug (7 ft x 7 ft) would be the most appropiate one since it fits in the room, only leaving a total uncovered area of 1 square foot to the sides.
Step-by-step explanation:
1. Calculate the total area that the different rugs can cover.
a. 7 ft x 7 ft (square): [tex]Area=s^{2} =(7ft)^{2} =49ft^{2}[/tex].
b. 8 ft diameter (circle): [tex]Area=\pi r^{2} =\pi (\frac{8ft}{2} )^{2}=50.27ft^{2}[/tex].
Note. We substituted the radius (r) by the length of the diamateter divided by 2 because the radius is just half of the diamaterer in a circle.
c. 6 ft x 8 1/2 ft (square): [tex]Area=w*l=(6ft)(8.5ft) =51ft^{2}[/tex].
2. Compare the total area that the different rugs can cover.
Taking into account that the room has an area of 50-square-foot, the 6 ft x 8 1/2 ft is not an option, since the rug is larger than the room. Also, the 8 ft diameter is barely larger than the room, so it isn't an option either. Therefore, the first rug, 7 ft x 7 ft, would be the most appropiate one since it fits in the room, only leaving a total uncovered area of 1 square foot to the sides.
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¿How much space is left uncovered?
If the room has a measure of 50 square-foot, the length of one side is [tex]\sqrt{50}[/tex] . Now, the difference between the height of this room and the rug is, approximately, [tex]0.0711[/tex]. If the rug is placed in the center of the room, there will be a space of [tex]\frac{0.0711}{2}= 0.0356[/tex] feet between the walls and the rug for each side.