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In the figure above, the grid consists of unit squares and P, Q and R

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In the figure above, the grid consists of unit squares and P, Q and R [#permalink]

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New post 09 Aug 2017, 02:04
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In the figure above, the grid consists of unit squares and P, Q and R are points of intersection of the grid as shown. What is the perimeter of triangular region PQR?

(A) 15
(B) 17
(C) 20
(D) 5 + 5√2
(E) 10 + 5√2

[Reveal] Spoiler:
Attachment:
2017-08-09_1257.png
2017-08-09_1257.png [ 6.37 KiB | Viewed 289 times ]
[Reveal] Spoiler: OA

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Re: In the figure above, the grid consists of unit squares and P, Q and R [#permalink]

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New post 09 Aug 2017, 02:11
Bunuel wrote:
Image
In the figure above, the grid consists of unit squares and P, Q and R are points of intersection of the grid as shown. What is the perimeter of triangular region PQR?

(A) 15
(B) 17
(C) 20
(D) 5 + 5√2
(E) 10 + 5√2

[Reveal] Spoiler:
Attachment:
2017-08-09_1257.png


Consider PR as hypotenuse of a right angled triangle with other sides as 4 and 3 then PR = 5
Consider QP as hypotenuse of a right angled triangle with other sides as 4 and 3 then QP = 5
Consider QR as hypotenuse of a right angled triangle with other sides as 1 and 7 then QR = \(5\sqrt{2}\)
PR + QP + QR = \(10 +5\sqrt{2}\)
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In the figure above, the grid consists of unit squares and P, Q and R [#permalink]

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New post 09 Aug 2017, 02:24
Bunuel wrote:
Image
In the figure above, the grid consists of unit squares and P, Q and R are points of intersection of the grid as shown. What is the perimeter of triangular region PQR?

(A) 15
(B) 17
(C) 20
(D) 5 + 5√2
(E) 10 + 5√2

[Reveal] Spoiler:
Attachment:
The attachment 2017-08-09_1257.png is no longer available


as is evident from the figure, we have right angle triangles, QRS, QTP, & PUR that will provide the length of sides QR, QP & PR.

For triangle QRS
side SR = 7 (number of columns between S & R)
Side QS = 1 (number of rows between Q & S)
therefore QR = \(\sqrt{(7^2+1^2)}\)= \(5\sqrt{2}\)

Similarly for triangle QTP
QT=3, TP=4, hence QP=5

and for triangle PUR
PU=3, UR=4, hence PR =5

So the perimeter of triangle PQR = 5+5+\(5\sqrt{2}\)= 10 + \(5\sqrt{2}\)
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triangle.jpg
triangle.jpg [ 31.17 KiB | Viewed 217 times ]

Kudos [?]: 245 [0], given: 33

In the figure above, the grid consists of unit squares and P, Q and R   [#permalink] 09 Aug 2017, 02:24
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In the figure above, the grid consists of unit squares and P, Q and R

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