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23 Nov 2022, 09:15
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D
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Difficulty:
65%
(hard)
Question Stats:
44% (02:41) correct
56%
(02:15)
wrong
based on 16
sessions
History
Date
Time
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Not Attempted Yet
In two equilateral parallelograms, X and Y, the sum of the lengths of the diagonals of X is equal to the sum of the lengths of the diagonals of Y. In X, the length of the longer diagonal is 20 more than the length of the shorter diagonal. In Y, the length of the longer diagonal is 8 more than the length of the shorter diagonal. What is the area of Y minus the area of X?
A. 336
B. 168
C. 84
D. 42
E. 0
A. 336
B. 168
C. 84
D. 42
E. 0
23 Nov 2022, 10:50
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Diagonals of X- x, x+20.
Diagonals of Y- y, y+8
Given: x+x+20=y+y+8, so y-x=6.
Now area of rhombus= (1/2)*product of diagonals
Required to find:
(1/2)y(y+8) - (1/2)x(x+20)
(1/2)(y^2+8y-x^2-20x)
(1/2)((y^2-x^2)+8y-20x)
(1/2)((y+x)(y-x)+8y-20x)
(1/2)((y+x)6+8y-20x) substitute y-x=6
(1/2)(6y+6x+8y-20x)
(1/2)(14y-14x)
(1/2)14(y-x) substitute y-x=6
(1/2)14*6
(1/2)(84)=42
Hence D is the correct choice.
Posted from my mobile device
Diagonals of Y- y, y+8
Given: x+x+20=y+y+8, so y-x=6.
Now area of rhombus= (1/2)*product of diagonals
Required to find:
(1/2)y(y+8) - (1/2)x(x+20)
(1/2)(y^2+8y-x^2-20x)
(1/2)((y^2-x^2)+8y-20x)
(1/2)((y+x)(y-x)+8y-20x)
(1/2)((y+x)6+8y-20x) substitute y-x=6
(1/2)(6y+6x+8y-20x)
(1/2)(14y-14x)
(1/2)14(y-x) substitute y-x=6
(1/2)14*6
(1/2)(84)=42
Hence D is the correct choice.
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23 Nov 2022, 22:56
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Bunuel
Equilateral parallelogram indicates that the quadrilateral is a Rhombus.
Area of Rhombus =\(\frac{ 1}{2}\) * product of diagonals
Given
Parallelogram : X
- Shorter Side: x
- Longer Side: x+20
Parallelogram : Y
- Shorter Side: y
- Longer Side: y+8
The sum of the lengths of the diagonals of X is equal to the sum of the lengths of the diagonals of Y
x + x + 20 = y + y + 8
x = y - 6
Question
\(\frac{1}{2} * y * (y+8) - 1/2 * x * (x+20)\)
Substituting x in terms of y
\([\frac{1}{2 }* y * (y+8)] - [\frac{1}{2} * (y-6) * (y + 14)]\)
\(\frac{1}{2}[y^2 + 8y - y^2 - 8y + (14*6)]\\
\)
\(14 * 3 = 42\)
Option D
