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

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In the xy-coordinate plane, triangle RST is equilateral. Points R and  [#permalink]

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New post 21 May 2019, 01:30
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  35% (medium)

Question Stats:

81% (01:08) correct 19% (01:19) wrong based on 45 sessions

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Re: In the xy-coordinate plane, triangle RST is equilateral. Points R and  [#permalink]

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New post 21 May 2019, 01:55
1
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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Re: In the xy-coordinate plane, triangle RST is equilateral. Points R and  [#permalink]

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New post 21 May 2019, 02:11
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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Re: In the xy-coordinate plane, triangle RST is equilateral. Points R and  [#permalink]

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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]

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New post 21 May 2019, 05:05
I used Pythagoras as we have a right triangle R0T.

〖0R〗^2+ 〖0T〗^2= 〖RT〗^2
1^2+ 2^2= 〖RT〗^2
√5= RT
Perimeter = 3RT so 3√5

Answer D
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Re: In the xy-coordinate plane, triangle RST is equilateral. Points R and  [#permalink]

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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]

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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?
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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]

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New post 21 May 2019, 18:17
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]

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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]

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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] 22 May 2019, 12:24
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