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In the figure below, what is the length of the perimeter of triangle O

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Bunuel
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In the figure below, what is the length of the perimeter of triangle O [#permalink] In the figure below, what is the length of the perimeter of triangle O   18 Dec 2020, 05:00
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E

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In the figure below, what is the length of the perimeter of triangle OPQ?



(A) \(\sqrt{7}\)

(B) 3

(C) \(\sqrt{5} + \sqrt{2}\)

(D) \(5 + 2\sqrt{2}\)

(E) \(2\sqrt{5} + \sqrt{2}\)



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E
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yashikaaggarwal
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Re: In the figure below, what is the length of the perimeter of triangle O [#permalink] In the figure below, what is the length of the perimeter of triangle O   18 Dec 2020, 07:19
Perimeter of triangle OPQ = Distance between OP + OQ + PQ
Distance = √(y2-y1)^2+(x2-x1)^2

Distance between OP = √(1-0)^2+(2-0)^2
=> √1+4
=> √5

Distance between OQ = √(2-0)^2+(1-0)^2
=> √4+1
=> √5

Distance between QP = √(2-1)^2+(1-2)^2
=> √1+1
=> √2

Perimeter will be √5 + √5 + √2
=> 2√5 + √2

Bunuel I guess the E option needs editing. Can you cross check
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Re: In the figure below, what is the length of the perimeter of triangle O [#permalink] In the figure below, what is the length of the perimeter of triangle O   18 Dec 2020, 07:32
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Quote:
In the figure below, what is the length of the perimeter of triangle OPQ?

Using the distance formula or Pythagoras theorem:
OP = \(\sqrt{5}\)
PQ = \(\sqrt{2} \)
OQ = \(\sqrt{5}\)

Perimeter = 2\(\sqrt{5}\) + \(\sqrt{2}\)

Option E must be 2\(\sqrt{5}\) + \(\sqrt{2}\) instead of 2\(\sqrt{5}\) +2
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Re: In the figure below, what is the length of the perimeter of triangle O [#permalink] In the figure below, what is the length of the perimeter of triangle O   18 Dec 2020, 09:03
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Using Pythagoras Theorem, to find the distance between \(PQ = 1^2+1^2 = \sqrt{2} \)

Ans E
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Re: In the figure below, what is the length of the perimeter of triangle O [#permalink]
18 Dec 2020, 09:03
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Bunuel
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