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20 Mar 2022, 02:51
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E
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Difficulty:
45%
(medium)
Question Stats:
63% (01:40) correct
38%
(01:24)
wrong
based on 64
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A piece of carpet in the shape of a trapezoid has a smaller base measuring 50 inches and the larger base measuring 70 inches. What is the perimeter of the carpet?
(1) The area of the carpet is 450 square inches.
(2) The height of the carpet is 7.5 inches.
Are You Up For the Challenge: 700 Level Questions
(1) The area of the carpet is 450 square inches.
(2) The height of the carpet is 7.5 inches.
Are You Up For the Challenge: 700 Level Questions
21 Mar 2022, 16:16
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Question: What is the perimeter of the carpet?
Need to know: The length of the other two sides
(1) The area of the carpet is 450 square inches.
Tells us nothing about the other two sides, we can only find the height which isn't sufficient.
(2) The height of the carpet is 7.5 inches.
Again we know nothing about the other two sides, basically repeats statement one.
The answer should be E unless there is some relationship I am unaware of.
Need to know: The length of the other two sides
(1) The area of the carpet is 450 square inches.
Tells us nothing about the other two sides, we can only find the height which isn't sufficient.
(2) The height of the carpet is 7.5 inches.
Again we know nothing about the other two sides, basically repeats statement one.
The answer should be E unless there is some relationship I am unaware of.
14 Jun 2023, 02:09
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A piece of carpet in the shape of a trapezoid has a smaller base measuring 50 inches and the larger base measuring 70 inches. What is the perimeter of the carpet?
(1) The area of the carpet is 450 square inches.
Let the perimeter be, P = 50 + 70 +s1 +s2
To determine s1 and s2, it is essential to determine whether the trapezoid is isosceles or otherwise.
1/2 * (50 + 70) * H = 450
So, H = 450/60 = 7.5
If isosceles, then s1 = s2 = sqrt (10^2 + 7.5^2) = 12.5
Hence, P = 50 + 70 + 12.5 +12.5 = 145.............(1)
If isosceles, then considering an arbitrary example,
s1 = sqrt (5^2 + 7.5^2) = sqrt (81.25) = 9.02 (approx)
s2 = sqrt (15^2 + 7.5^2) = sqrt (281.25) = 16.90 (approx)
Hence, P = 50 + 70 + 9.02 +16.90 = 145.92 = 146 (approx).............(2)
There will be difference in Perimeter for cases (1) & (2) (though small difference)
So, Perimeter can't be uniquely determined.
(2) The height of the carpet is 7.5 inches.
Already given in this case, H = 7.5
(explananation same as above)
If isosceles, then s1 = s2 = sqrt (10^2 + 7.5^2) = 12.5
Hence, P = 50 + 70 + 12.5 +12.5 = 145.............(1)
If isosceles, then considering an arbitrary example,
s1 = sqrt (5^2 + 7.5^2) = sqrt (81.25) = 9.02 (approx)
s2 = sqrt (15^2 + 7.5^2) = sqrt (281.25) = 16.90 (approx)
Hence, P = 50 + 70 + 9.02 +16.90 = 145.92 = 146 (approx).............(2)
There will be difference in Perimeter for cases (1) & (2) (though small difference)
So, Perimeter can't be uniquely determined.
Using (1) & (2) together,
(1) The area of the carpet is 450 square inches.
(2) The height of the carpet is 7.5 inches.
No extra information is gained, since both the prompts lead to H = 7.5
So, Perimeter can't be uniquely determined.
(E) is the answer
(1) The area of the carpet is 450 square inches.
Let the perimeter be, P = 50 + 70 +s1 +s2
To determine s1 and s2, it is essential to determine whether the trapezoid is isosceles or otherwise.
1/2 * (50 + 70) * H = 450
So, H = 450/60 = 7.5
If isosceles, then s1 = s2 = sqrt (10^2 + 7.5^2) = 12.5
Hence, P = 50 + 70 + 12.5 +12.5 = 145.............(1)
If isosceles, then considering an arbitrary example,
s1 = sqrt (5^2 + 7.5^2) = sqrt (81.25) = 9.02 (approx)
s2 = sqrt (15^2 + 7.5^2) = sqrt (281.25) = 16.90 (approx)
Hence, P = 50 + 70 + 9.02 +16.90 = 145.92 = 146 (approx).............(2)
There will be difference in Perimeter for cases (1) & (2) (though small difference)
So, Perimeter can't be uniquely determined.
(2) The height of the carpet is 7.5 inches.
Already given in this case, H = 7.5
(explananation same as above)
If isosceles, then s1 = s2 = sqrt (10^2 + 7.5^2) = 12.5
Hence, P = 50 + 70 + 12.5 +12.5 = 145.............(1)
If isosceles, then considering an arbitrary example,
s1 = sqrt (5^2 + 7.5^2) = sqrt (81.25) = 9.02 (approx)
s2 = sqrt (15^2 + 7.5^2) = sqrt (281.25) = 16.90 (approx)
Hence, P = 50 + 70 + 9.02 +16.90 = 145.92 = 146 (approx).............(2)
There will be difference in Perimeter for cases (1) & (2) (though small difference)
So, Perimeter can't be uniquely determined.
Using (1) & (2) together,
(1) The area of the carpet is 450 square inches.
(2) The height of the carpet is 7.5 inches.
No extra information is gained, since both the prompts lead to H = 7.5
So, Perimeter can't be uniquely determined.
(E) is the answer
