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Swimming Pool A has a perimeter of 100 meters. Swimming Pool B has a
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21 Dec 2022, 11:33
21 Dec 2022, 11:33
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56% (01:13) correct
44% (01:56) wrong based on 25 sessions
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Swimming Pool A has a perimeter of 100 meters. Swimming Pool B has a perimeter of 80 meters. Both swimming pools are rectangular.
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
The area of Swimming Pool A, in square meters |
The area of Swimming Pool B, in square meters |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Re: Swimming Pool A has a perimeter of 100 meters. Swimming Pool B has a
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23 Dec 2022, 05:00
23 Dec 2022, 05:00
Expert Reply
OE
Even though both swimming pools are rectangular and Swimming Pool A has a larger perimeter, it is possible for Swimming Pool 8 to cover a larger area or the same area as Swimming Pool A. For example, Swimming Pool A could have a length of 40 meters and a width of 10 meters (Perimeter = 2 x length + 2 x width for rectangles). This would give Swimming Pool A an area of 40 x 10 = 400 square meters. If Swimming Pool 8 is square, its area would be maximized at 80/4=20^2=400 equal to that of Swimming Pool A. If instead Swimming Pool 8 had a length of 30 meters and a width of 10 meters, its area would equal 30 x 10 = 300 square meters.
It is also possible to construct examples in which Swimming Pool A has a smaller area than Pool B. Thus, the relationship cannot be determined from the informationì given.
Even though both swimming pools are rectangular and Swimming Pool A has a larger perimeter, it is possible for Swimming Pool 8 to cover a larger area or the same area as Swimming Pool A. For example, Swimming Pool A could have a length of 40 meters and a width of 10 meters (Perimeter = 2 x length + 2 x width for rectangles). This would give Swimming Pool A an area of 40 x 10 = 400 square meters. If Swimming Pool 8 is square, its area would be maximized at 80/4=20^2=400 equal to that of Swimming Pool A. If instead Swimming Pool 8 had a length of 30 meters and a width of 10 meters, its area would equal 30 x 10 = 300 square meters.
It is also possible to construct examples in which Swimming Pool A has a smaller area than Pool B. Thus, the relationship cannot be determined from the informationì given.
Swimming Pool A has a perimeter of 100 meters. Swimming Pool B has a
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30 Jan 2024, 21:02
30 Jan 2024, 21:02
1
For a given perimeter, the square maximizes the area.
You can therefore create rectangles for a given perimeter with the smallest possible area to the greatest possible area.
Since the two perimeters are not too far from each other, 100 and 80, it is quite possible to create rectangles to ensure that the Area of A is greater than, equal to or less than the area of B.
For example, keeping the perimeter of A=100 and B=80, the following scenarios are possible.
1. If A is a square with each side equal to 25, we get an area of 625 which is greater than 400, which will be the area of a B if it is a square and each side is equal to 20.
2. But if the sides of A are 10 and 40, we get an area of 400 which is equal to the area of B when each of its side is equal to 20.
3. If the sides of A are 45 and 5, its area is 225 which is less than 300, which will be the area of B if each of its sides are 10 and 30
Hence no relationship exists between Quantity A and Quantity B.
The answer is D.
You can therefore create rectangles for a given perimeter with the smallest possible area to the greatest possible area.
Since the two perimeters are not too far from each other, 100 and 80, it is quite possible to create rectangles to ensure that the Area of A is greater than, equal to or less than the area of B.
For example, keeping the perimeter of A=100 and B=80, the following scenarios are possible.
1. If A is a square with each side equal to 25, we get an area of 625 which is greater than 400, which will be the area of a B if it is a square and each side is equal to 20.
2. But if the sides of A are 10 and 40, we get an area of 400 which is equal to the area of B when each of its side is equal to 20.
3. If the sides of A are 45 and 5, its area is 225 which is less than 300, which will be the area of B if each of its sides are 10 and 30
Hence no relationship exists between Quantity A and Quantity B.
The answer is D.
