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A thin piece of cable 90 meters long is cut into two pieces.

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PareshGmat
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A thin piece of cable 90 meters long is cut into two pieces. [#permalink] New post   12 Nov 2014, 19:48
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A thin piece of cable 90 meters long is cut into two pieces. One piece is used to form a square with diagonal \(\sqrt{72}\), and the other is used to form a equilateral triangle. 6 meters cable is left over. The total area, in square meters, of the square and equilateral triangle regions would be

A: \(24 + 100\sqrt{3}\)

B: \(36 + 20\sqrt{3}\)

C: \(36 + 50\sqrt{3}\)

D: \(\sqrt{3}(100 + 12\sqrt{3})\)

E: \(42 + 100\sqrt{3}\)
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Bhanupriyachauhan
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Re: A thin piece of cable 90 meters long is cut into two pieces. [#permalink] New post   12 Nov 2014, 20:55
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Diagonal of square = √72
So side of square = 1/√2 *√72
= 6
Area of square = 6*6 = 36
Perimeter of square = 4*6 = 24
Total length = 90
Perimeter of equilateral triangle = 90-24-6 = 60
So 3a = 60
a = 20
Where a is the side of the equilateral triangle.
Area of equilateral triangle = √3/4*20*20
= 100√3
So area of square + area of equilateral triangle = 36 + 100√3=
√3(100+12√3)

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Re: A thin piece of cable 90 meters long is cut into two pieces. [#permalink] New post   13 Nov 2014, 07:04
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PareshGmat wrote:
A thin piece of cable 90 meters long is cut into two pieces. One piece is used to form a square with diagonal \(\sqrt{72}\), and the other is used to form a equilateral triangle. 6 meters cable is left over. The total area, in square meters, of the square and equilateral triangle regions would be

A: \(24 + 100\sqrt{3}\)

B: \(36 + 20\sqrt{3}\)

C: \(36 + 50\sqrt{3}\)

D: \(\sqrt{3}(100 + 12\sqrt{3})\)

E: \(42 + 100\sqrt{3}\)



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Re: A thin piece of cable 90 meters long is cut into two pieces. [#permalink] New post   12 May 2021, 02:26
Bhanupriyachauhan wrote:
Diagonal of square = √72
So side of square = 1/√2 *√72
= 6
Area of square = 6*6 = 36
Perimeter of square = 4*6 = 24
Total length = 90
Perimeter of equilateral triangle = 90-24-6 = 60
So 3a = 60
a = 20
Where a is the side of the equilateral triangle.
Area of equilateral triangle = √3/4*20*20
= 100√3
So area of square + area of equilateral triangle = 36 + 100√3=
√3(100+12√3)

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Perimeter of equilateral triangle should be = Length of wire - Perimeter of square = 90 - 24 = 66
Kindly explain why subtract additional 6 from this equation.
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MBAB123
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Re: A thin piece of cable 90 meters long is cut into two pieces. [#permalink] New post   12 May 2021, 06:10
Medha011 wrote:
Bhanupriyachauhan wrote:
Diagonal of square = √72
So side of square = 1/√2 *√72
= 6
Area of square = 6*6 = 36
Perimeter of square = 4*6 = 24
Total length = 90
Perimeter of equilateral triangle = 90-24-6 = 60
So 3a = 60
a = 20
Where a is the side of the equilateral triangle.
Area of equilateral triangle = √3/4*20*20
= 100√3
So area of square + area of equilateral triangle = 36 + 100√3=
√3(100+12√3)

Posted from my mobile device


Perimeter of equilateral triangle should be = Length of wire - Perimeter of square = 90 - 24 = 66
Kindly explain why subtract additional 6 from this equation.

Medha011
It is given in the question that 6m wire is leftover therefore we subtract 6 as well
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Re: A thin piece of cable 90 meters long is cut into two pieces. [#permalink]
12 May 2021, 06:10
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