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The length of the diagonal of square S, as well as the lengths of the
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25 Aug 2022, 09:47
25 Aug 2022, 09:47
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Question Stats:
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The length of the diagonal of square S, as well as the lengths of the diagonals of rhombus R are integers. The ratio of the lengths of the diagonals is 15:11:9, respectively. Which of the following could be the difference between the area of square S and the area of rhombus R?
I. 63
II. 126
III. 252
A. I only
B. II only
C. III only
D. I and III only
E. I, II and III
I. 63
II. 126
III. 252
A. I only
B. II only
C. III only
D. I and III only
E. I, II and III
Part of the project: GRE QCQ & PS 3 Questions Every One DAILY Challenge - (2022)
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GRE Math Essentials (2022)
GRE Geometry Formulas
GRE - Math Book
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GRE Math Essentials (2022)
GRE Geometry Formulas
GRE - Math Book
The length of the diagonal of square S, as well as the lengths of the
[#permalink]
25 Aug 2022, 10:02
25 Aug 2022, 10:02
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Let the diagnol of square be d1; the two diagnols of rhombus be d2,d3 respectively.
If side of square is s;
d1 = \sqrt{2}[/m]
Squaring both sides
s*s = d1*d1/2
Area of rhombus in terms of diagnols = d2*d3/2
To estimate,
A = Area of square - Area of rhombus
A = d1*d1/2 - d2*d3/2
Given ratio, d1:d2:d3 = 15:11:9
Let common ratio be x, d1 = 15x, d2 = 11x, d3 = 9x
So, A = 63x*x
When x = 1, A = 63
When x =2 , A = 252
When x = \sqrt{2}, A= 126
Since diagnol lengths are integers, x has to be an integer; I and III are possible and II is not
Answer is D
If side of square is s;
d1 = \sqrt{2}[/m]
Squaring both sides
s*s = d1*d1/2
Area of rhombus in terms of diagnols = d2*d3/2
To estimate,
A = Area of square - Area of rhombus
A = d1*d1/2 - d2*d3/2
Given ratio, d1:d2:d3 = 15:11:9
Let common ratio be x, d1 = 15x, d2 = 11x, d3 = 9x
So, A = 63x*x
When x = 1, A = 63
When x =2 , A = 252
When x = \sqrt{2}, A= 126
Since diagnol lengths are integers, x has to be an integer; I and III are possible and II is not
Answer is D
The length of the diagonal of square S, as well as the lengths of the
[#permalink]
25 Aug 2022, 20:28
25 Aug 2022, 20:28
Thanks.
