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04 Aug 2021, 01:30
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Difficulty:
45%
(medium)
Question Stats:
73% (02:11) correct
27%
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wrong
based on 106
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The height of an equilateral triangle is the side of a smaller equilateral triangle, as shown above. If the side of the large equilateral triangle is 1, what is AB?
A. 1 - √3/2
B. 0.25
C. 2 - √3
D. 1/3
E. 1 - √3/4
Attachment:
1.png [ 4.28 KiB | Viewed 3009 times ]
04 Aug 2021, 01:39
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Explanation:
a = side of larger triangle
The altitude of larger Equilateral Triangle = (1/2)*√3*a = √3/2 = side of smaller triangle.
b = side of smaller triangle
The altitude of smaller Equilateral Triangle = (1/2)*√3*b = 3/4
AB length = 1 - 3/4
=0.25
IMO-B
a = side of larger triangle
The altitude of larger Equilateral Triangle = (1/2)*√3*a = √3/2 = side of smaller triangle.
b = side of smaller triangle
The altitude of smaller Equilateral Triangle = (1/2)*√3*b = 3/4
AB length = 1 - 3/4
=0.25
IMO-B
asishron29181
Joined: 04 May 2020
Last visit: 04 Nov 2022
Posts: 185
Given Kudos: 68
Location: India
Schools: Great Lakes (I)
GMAT 1: 610 Q47 V27
WE:Programming (Computer Software)
04 Aug 2021, 04:35
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Length of longest equilateral triangle = 1
Height of long triangle = √3/2 * 1 = √3/2
Length of smaller triangle = √3/2
Height of smaller triangle= √3/2 * √3/2 = 3/4
Now the length of AB = Length of bigger equilateral triangle - Length of height of smaller triangle = 1 - 0.75 = 0.25
IMO B
Height of long triangle = √3/2 * 1 = √3/2
Length of smaller triangle = √3/2
Height of smaller triangle= √3/2 * √3/2 = 3/4
Now the length of AB = Length of bigger equilateral triangle - Length of height of smaller triangle = 1 - 0.75 = 0.25
IMO B
