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In the xy-coordinate plane, triangle RST is equilateral. Points R and

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Bunuel
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In the xy-coordinate plane, triangle RST is equilateral. Points R and [#permalink] New post   21 May 2019, 01:30
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In the xy-coordinate plane, triangle RST is equilateral. Points R and T have coordinates (0, 2) and (1, 0), respectively. What is the perimeter of triangle RST?

A. \(\sqrt{5}\)
B. \(3\sqrt{3}\)
C. \(6\)
D. \(3\sqrt{5}\)
E. 9
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KarishmaB
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Re: In the xy-coordinate plane, triangle RST is equilateral. Points R and [#permalink] New post   21 May 2019, 01:55
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Bunuel wrote:
In the xy-coordinate plane, triangle RST is equilateral. Points R and T have coordinates (0, 2) and (1, 0), respectively. What is the area of triangle RST?

A. \sqrt{5}
B. \(3\sqrt{3}\)
C. \(6\)
D. \(3\sqrt{5}\)
E. 9


Area of equilateral triangle \(= \sqrt{3}s^2/4\)

The length of the side s \(= \sqrt{(0 - 1)^2 + (2 - 0)^2} = \sqrt{5}\)

Area of triangle \(= \sqrt{3}(\sqrt{5})^2/4 = 5\sqrt{3}/4\)
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Bunuel
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Re: In the xy-coordinate plane, triangle RST is equilateral. Points R and [#permalink] New post   21 May 2019, 02:11
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VeritasKarishma wrote:
Bunuel wrote:
In the xy-coordinate plane, triangle RST is equilateral. Points R and T have coordinates (0, 2) and (1, 0), respectively. What is the area of triangle RST?

A. \sqrt{5}
B. \(3\sqrt{3}\)
C. \(6\)
D. \(3\sqrt{5}\)
E. 9


Area of equilateral triangle \(= \sqrt{3}s^2/4\)

The length of the side s \(= \sqrt{(0 - 1)^2 + (2 - 0)^2} = \sqrt{5}\)

Area of triangle \(= \sqrt{3}(\sqrt{5})^2/4 = 5\sqrt{3}/4\)


The question actually asks about the perimeter, not the area. Edited. Thank you.
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nick1816
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Re: In the xy-coordinate plane, triangle RST is equilateral. Points R and [#permalink] New post   21 May 2019, 03:14
Length of RT=[(0-1)^2 + (2-0)^2]^{1/2}=5^{1/2}
Perimeter of equilateral triangle=3*side= 3*5^{1/2}
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Re: In the xy-coordinate plane, triangle RST is equilateral. Points R and [#permalink] New post   21 May 2019, 06:19
Bunuel wrote:
In the xy-coordinate plane, triangle RST is equilateral. Points R and T have coordinates (0, 2) and (1, 0), respectively. What is the perimeter of triangle RST?

A. \(\sqrt{5}\)
B. \(3\sqrt{3}\)
C. \(6\)
D. \(3\sqrt{5}\)
E. 9



I used the distrance formula
\(\sqrt{(x2 - x1)^2 + (y2-y1)^2}\)

since this is an equilateral triangle
perimeter will be 3 * side

3\sqrt{5}
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Re: In the xy-coordinate plane, triangle RST is equilateral. Points R and [#permalink] New post   Updated on: 22 May 2019, 01:58
Bunuel wrote:
In the xy-coordinate plane, triangle RST is equilateral. Points R and T have coordinates (0, 2) and (1, 0), respectively. What is the perimeter of triangle RST?

A. \(\sqrt{5}\)
B. \(3\sqrt{3}\)
C. \(6\)
D. \(3\sqrt{5}\)
E. 9


use distance formula each side = √5
perimeter ; \(3\sqrt{5}\)
IMO D

Bunuel is the published answer option correct? how can perimeter be 6?

Originally posted by Archit3110 on 21 May 2019, 08:12.
Last edited by Archit3110 on 22 May 2019, 01:58, edited 1 time in total.
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Re: In the xy-coordinate plane, triangle RST is equilateral. Points R and [#permalink] New post   21 May 2019, 18:17
Hi, Bunuel,
OA is 6. Can you please explain c as an answer?

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Re: In the xy-coordinate plane, triangle RST is equilateral. Points R and [#permalink] New post   21 May 2019, 18:19
Bunuel wrote:
In the xy-coordinate plane, triangle RST is equilateral. Points R and T have coordinates (0, 2) and (1, 0), respectively. What is the perimeter of triangle RST?

A. \(\sqrt{5}\)
B. \(3\sqrt{3}\)
C. \(6\)
D. \(3\sqrt{5}\)
E. 9

Hi, Bunuel,
OA is 6. Can you please explain c as an answer?

Posted from my mobile device
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Re: In the xy-coordinate plane, triangle RST is equilateral. Points R and [#permalink] New post   22 May 2019, 12:24
Can anyone please explain how the answer is c) 6 and not d)3√5
Thanks

[size=80][b][i]Posted from my mobile device[/i][/b][/size]
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Re: In the xy-coordinate plane, triangle RST is equilateral. Points R and [#permalink] New post   26 Apr 2023, 12:35
the distance between R and T is sqrt(5). since it is equilateral triangle, all the sides are sqrt(5). The perimeter thus is 3 x sqrt(5).
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Re: In the xy-coordinate plane, triangle RST is equilateral. Points R and [#permalink]
26 Apr 2023, 12:35
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