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Square and an equilateral triangle each have sides of length
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24 Jan 2019, 06:56
24 Jan 2019, 06:56
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Question Stats:
86% (01:26) correct
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Square and an equilateral triangle each have sides of length 5. What is the ratio of the area of the square to the area of the triangle?
A. \(\frac{4}{3}\)
B. \(\frac{16}{9}\)
C. \(\frac{3}{4}\)
D. \(\frac{4\sqrt{3}}{3}\)
E. \(\frac{16\sqrt{3}}{9}\)
A. \(\frac{4}{3}\)
B. \(\frac{16}{9}\)
C. \(\frac{3}{4}\)
D. \(\frac{4\sqrt{3}}{3}\)
E. \(\frac{16\sqrt{3}}{9}\)
Re: Square and an equilateral triangle each have sides of length
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25 Jan 2019, 03:18
25 Jan 2019, 03:18
1
area of the square = 25
area of the equilateral triangle = \(\sqrt{3}/4 * 25\)
\(\frac{25}{25 * \sqrt{3}/4}\)
cancel 25 to get \(4/\sqrt{3}\)
among ans choices option D can be reduced to \(4/\sqrt{3}\) this is because \(\sqrt{3}*\sqrt{3} = 3\)
area of the equilateral triangle = \(\sqrt{3}/4 * 25\)
\(\frac{25}{25 * \sqrt{3}/4}\)
cancel 25 to get \(4/\sqrt{3}\)
among ans choices option D can be reduced to \(4/\sqrt{3}\) this is because \(\sqrt{3}*\sqrt{3} = 3\)
Re: Square and an equilateral triangle each have sides of length
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25 Jan 2019, 09:10
25 Jan 2019, 09:10
Expert Reply
Carcass wrote:
Square and an equilateral triangle each have sides of length 5. What is the ratio of the area of the square to the area of the triangle?
A. \(\frac{4}{3}\)
B. \(\frac{16}{9}\)
C. \(\frac{3}{4}\)
D. \(\frac{4\sqrt{3}}{3}\)
E. \(\frac{16\sqrt{3}}{9}\)
A. \(\frac{4}{3}\)
B. \(\frac{16}{9}\)
C. \(\frac{3}{4}\)
D. \(\frac{4\sqrt{3}}{3}\)
E. \(\frac{16\sqrt{3}}{9}\)
Area of square = \(a^2\)
Area of equilateral triangle =\(a^2\frac{\sqrt{3}}{4}\)
ratio of the area of the square to the area of the triangle = \(a^2\):\(a^2\frac{\sqrt{3}}{4}\)=1:\(\frac{\sqrt{3}}{4}\)=\(\frac{4}{\sqrt{3}}\)=\(\frac{4\sqrt{3}}{3}\)
So, irrespective of the dimension of side, the ratio will remain the same.
