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04 Nov 2020, 02:30
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A
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Difficulty:
45%
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Question Stats:
70% (02:17) correct
30%
(02:33)
wrong
based on 40
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Two identical regular hexagons are inscribed in a rectangle whose area is 256√3 square inches. What is the perimeter of each hexagon in inches?
A. 48
B. 56
C. 64
D. 56√3
E. 64√3
Attachment:
1.png [ 9.87 KiB | Viewed 3600 times ]
yashikaaggarwal
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04 Nov 2020, 02:55
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Given the figure is rectangle.
The area is = Length*Breadth
L*B = 256√3
Where the length of rectangle = 4*side of hexagon
Breath = 2*Side of hexagon√3/2
=> Side*hexagon√3
(30-60-90 triangle property)
L*B = 4√3*Side of hexagon^2
256√3 = 4√3*Side of hexagon^2
64 = Side of Hexagon^2
±8 = Side of Hexagon
Since side can't be negative
Side of hexagon is 8
Perimeter = 6*8 = 48
Answer is A
Posted from my mobile device
The area is = Length*Breadth
L*B = 256√3
Where the length of rectangle = 4*side of hexagon
Breath = 2*Side of hexagon√3/2
=> Side*hexagon√3
(30-60-90 triangle property)
L*B = 4√3*Side of hexagon^2
256√3 = 4√3*Side of hexagon^2
64 = Side of Hexagon^2
±8 = Side of Hexagon
Since side can't be negative
Side of hexagon is 8
Perimeter = 6*8 = 48
Answer is A
Posted from my mobile device
04 Nov 2020, 05:47
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A hexagon is made up of 6 equilateral triangles.
Let each side = a. Therefore the length of the hexagon is 4a
The breadth of the rectangle = 2 * height of the hexagon
Height = Height of the equilateral triangle = \(\frac{\sqrt{3}}{2}\)a
Therefore the breadth of the rectangle = \(2 *\frac{\sqrt{3}}{2}\) * a = \(\sqrt{3}\)a
Area of the rectangle = 4a * \(\sqrt{3}\)a = 256\(\sqrt{3}\)
4\(a^2\) = 256
\(a^2 = 64\)
a = 8
Perimeter of the hexagon = 6a = 6*8 = 48
Option A
Arun Kumar
Let each side = a. Therefore the length of the hexagon is 4a
The breadth of the rectangle = 2 * height of the hexagon
Height = Height of the equilateral triangle = \(\frac{\sqrt{3}}{2}\)a
Therefore the breadth of the rectangle = \(2 *\frac{\sqrt{3}}{2}\) * a = \(\sqrt{3}\)a
Area of the rectangle = 4a * \(\sqrt{3}\)a = 256\(\sqrt{3}\)
4\(a^2\) = 256
\(a^2 = 64\)
a = 8
Perimeter of the hexagon = 6a = 6*8 = 48
Option A
Arun Kumar
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hexagon.jpg [ 1.04 MiB | Viewed 3267 times ]
04 Nov 2020, 18:08
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@ 
1.png [ 13.55 KiB | Viewed 3153 times ]
We have 16 similar equilateral triangles( inside rectangle) whose side (a) is equal to side of regular hexagon.
\(16* \frac{\sqrt{3}*a^2}{4} = 256\sqrt{3}\)
a=8
Perimeter of regular hexagon = 6*8=48
Attachment:
1.png [ 13.55 KiB | Viewed 3153 times ]
We have 16 similar equilateral triangles( inside rectangle) whose side (a) is equal to side of regular hexagon.
\(16* \frac{\sqrt{3}*a^2}{4} = 256\sqrt{3}\)
a=8
Perimeter of regular hexagon = 6*8=48
