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ABCD is a square with side length 12 ∠CEF is a right angle D
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04 Jan 2021, 10:47
04 Jan 2021, 10:47
Expert Reply
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91% (02:53) correct
8% (02:41) wrong based on 45 sessions
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\(ABCD\) is a square with side length 12
\(∠CEF\) is a right angle
\(DE = 5\)
\(FB = 9
\)
Quantity A |
Quantity B |
Perimeter of \(\triangle DEC\) |
Perimeter of \(\triangle FEC\) |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Kudos for the right answer and explanation
Re: ABCD is a square with side length 12 ∠CEF is a right angle D
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05 Jan 2021, 13:49
05 Jan 2021, 13:49
1
A) perimeter of triangle DEC is consisted of , DC + DE + EC
B) perimeter of triangle FEC is consisted of , FC + EF + EC
both items includes length of EC, so we can cancel the length of EC to compare
A) DC+DE = 12 + 5 = 17
As FB : BC = 9:12 = 3:4, FC should be 5x3=15
B) FC + EF = 15 + sqrt ( (12-5) ^2 + 3^2 ) = 15 + sqrt(58)
A) 17,
B) 15 + sqrt(58)
sqrt(58) is obviously bigger than 2 which is calculated by 17-5, so B) is bigger.
Answer: B)
B) perimeter of triangle FEC is consisted of , FC + EF + EC
both items includes length of EC, so we can cancel the length of EC to compare
A) DC+DE = 12 + 5 = 17
As FB : BC = 9:12 = 3:4, FC should be 5x3=15
B) FC + EF = 15 + sqrt ( (12-5) ^2 + 3^2 ) = 15 + sqrt(58)
A) 17,
B) 15 + sqrt(58)
sqrt(58) is obviously bigger than 2 which is calculated by 17-5, so B) is bigger.
Answer: B)
Re: ABCD is a square with side length 12 ∠CEF is a right angle D
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09 Jan 2021, 23:40
09 Jan 2021, 23:40
1
The question has already been solved above. Mine is more of an observation based solution that requires no calculations.
The triangles in question share EC as a side. The difference being that for DEC, it is the hypotenuse and for FEC, it is not. Now, the hypotenuse is always the biggest side in a triangle and in FEC, CF will be bigger than the other two side. Therefore, the perimeter of FEC will be greater than that of DEC
The triangles in question share EC as a side. The difference being that for DEC, it is the hypotenuse and for FEC, it is not. Now, the hypotenuse is always the biggest side in a triangle and in FEC, CF will be bigger than the other two side. Therefore, the perimeter of FEC will be greater than that of DEC
