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

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

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21 May 2019, 01:30
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25% (medium)

Question Stats:

82% (01:07) correct 18% (01:23) wrong based on 65 sessions

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

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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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21 May 2019, 02:11
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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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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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

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

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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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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]

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21 May 2019, 18:17
Hi, Bunuel,

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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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,

Posted from my mobile device
_________________
Thanks in the forum can be expressed by hitting KUDOS!!!
Intern
Joined: 22 Apr 2019
Posts: 3
Re: In the xy-coordinate plane, triangle RST is equilateral. Points R and  [#permalink]

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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]
Re: In the xy-coordinate plane, triangle RST is equilateral. Points R and   [#permalink] 22 May 2019, 12:24
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