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30 Apr 2020, 02:02
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C
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Difficulty:
85%
(hard)
Question Stats:
53% (03:26) correct
47%
(02:45)
wrong
based on 59
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A square is inscribed in an equilateral triangle as shown above. What is the ratio of the area of the square to that of the equilateral triangle?
A. \(4: (12 + 15√3)\)
B. \(6 : (6 + 5√3)\)
C. \(12 : (12 + 7√3)\)
D. \(18 : (12 + 15√3)\)
E. \(24 : (24 + 7√3)\)
Are You Up For the Challenge: 700 Level Questions
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Untitled.png [ 5.19 KiB | Viewed 30446 times ]
ArunSharma12
Joined: 25 Oct 2015
Last visit: 20 Jul 2022
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Location: India
Schools: IIML-IPMX '22 (A)
GMAT 1: 650 Q48 V31
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30 Apr 2020, 02:23
Kudos
Bookmarks
A square is inscribed in an equilateral triangle as shown above. What is the ratio of the area of the square to that of the equilateral triangle?
A. 4:(12+15√3)
B. 6:(6+5√3)
C. 12:(12+7√3)
D. 18:(12+15√3)
E. 24:(24+7√3)
img.png [ 8.03 KiB | Viewed 27854 times ]
angles of the triangle mentioned in the figure are in ratio 30:60:90 so the sides will be in the ratio x:√3x:2x.
side of equilateral triangle = 2x +√3x
side of square = √3x
Area(square)/Area(Equilateral triangle) = \(\frac{(x√3)^2*4}{(2x+√3x)^2*√3}\) = \(\frac{3x^2*4}{x^2*(7+4√3)*√3}\) = \(\frac{4√3}{(7+4√3)}=\frac{12}{(7√3+12)}\)
Ans: C
A. 4:(12+15√3)
B. 6:(6+5√3)
C. 12:(12+7√3)
D. 18:(12+15√3)
E. 24:(24+7√3)
Attachment:
img.png [ 8.03 KiB | Viewed 27854 times ]
side of equilateral triangle = 2x +√3x
side of square = √3x
Area(square)/Area(Equilateral triangle) = \(\frac{(x√3)^2*4}{(2x+√3x)^2*√3}\) = \(\frac{3x^2*4}{x^2*(7+4√3)*√3}\) = \(\frac{4√3}{(7+4√3)}=\frac{12}{(7√3+12)}\)
Ans: C
30 Apr 2020, 05:17
Kudos
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See attached self-explanatory sketch. Let side of the square be a
Square area = a^2
Triangle:
base= a*(1+2/√3)
height= a*(1+ √3 /2)
area= a^2 *(1+ 7√3 /12)
Square area/ Triangle area
= a^2 / {a^2 *(1+ 7√3 /12)}
= 1 / (1+ 7√3 /12)
= 12 / (12+ 7√3)
FINAL ANSWER IS (C)
Posted from my mobile device
Square area = a^2
Triangle:
base= a*(1+2/√3)
height= a*(1+ √3 /2)
area= a^2 *(1+ 7√3 /12)
Square area/ Triangle area
= a^2 / {a^2 *(1+ 7√3 /12)}
= 1 / (1+ 7√3 /12)
= 12 / (12+ 7√3)
FINAL ANSWER IS (C)
Posted from my mobile device
Attachments
IMG_20200430_190918.jpg [ 557.33 KiB | Viewed 26652 times ]
