Bunuel wrote:
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
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 + \(5\sqrt{2}\)
Attachments
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