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Joined: 16 Apr 2020
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A sheet of paper ABDE is a 12in x 18in rectangle (Figure 1). The sheet
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17 Aug 2021, 08:16
17 Aug 2021, 08:16
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Question Stats:
33% (03:43) correct
66% (03:07) wrong based on 15 sessions
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A sheet of paper ABDE is a 12in x 18in rectangle.png [ 14.85 KiB | Viewed 1798 times ]
A sheet of paper ABDE is a 12in x 18in rectangle (Figure 1). The sheet is then folded along the segment CF so that points A and D coincide after the paper is folded (Figure 2)
NOTE: The shaded area represents a portion of the back side of the paper, not visible in Figure 1.
Quantity A |
Quantity B |
Area (in square inches) of the shaded region |
\(78\) |
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
Retired Moderator
Joined: 16 Apr 2020
Status:Founder & Quant Trainer
Affiliations: Prepster Education
Posts: 1546
Given Kudos: 172
Location: India
WE:Education (Education)
Re: A sheet of paper ABDE is a 12in x 18in rectangle (Figure 1). The sheet
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22 Aug 2021, 22:27
22 Aug 2021, 22:27
1
Explanation:
If we notice the shaded area is a triangle with area \(\frac{1}{2}(AF)(12)\)
NOTE: The height would be width of the given rectangle.
So,
Col. A: \(\frac{1}{2}(AF)(12)\)
Col. B: \(78\)
Col. A: \(AF\)
Col. B: \(\frac{78(2)}{12} = 13\)
Now,
Let \(EF = x\) so \(AF = (18 - x)\)
Applying Pythagoras theorem in triangle AFE;
\(AF^2 = AE^2 + EF^2\)
\((18 - x)^2 = 12^2 + x^2\)
\(324 + x^2 - 36x = 144 + x^2\)
\(180 = 36x\)
\(x = 5\)
Thus, \(AF = 18 - 5 = 13\)
Col. A: \(13\)
Col. B: \(13\)
Hence, option C
If we notice the shaded area is a triangle with area \(\frac{1}{2}(AF)(12)\)
NOTE: The height would be width of the given rectangle.
So,
Col. A: \(\frac{1}{2}(AF)(12)\)
Col. B: \(78\)
Col. A: \(AF\)
Col. B: \(\frac{78(2)}{12} = 13\)
Now,
Let \(EF = x\) so \(AF = (18 - x)\)
Applying Pythagoras theorem in triangle AFE;
\(AF^2 = AE^2 + EF^2\)
\((18 - x)^2 = 12^2 + x^2\)
\(324 + x^2 - 36x = 144 + x^2\)
\(180 = 36x\)
\(x = 5\)
Thus, \(AF = 18 - 5 = 13\)
Col. A: \(13\)
Col. B: \(13\)
Hence, option C
General Discussion
Re: A sheet of paper ABDE is a 12in x 18in rectangle (Figure 1). The sheet
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20 Aug 2021, 03:25
20 Aug 2021, 03:25
sir please explain.
