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

Question

https://gmatclub.com/forum/download/file.php?id=36819 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 2017-08-09_1257.png

Luckisnoexcuse · Answer

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} 
E

niks18 · Answer

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}

EgmatQuantExpert · Answer

Solution

Given  
 • In the figure above, the grid consists of unit squares
• P, Q and R are points of intersection of the grid as shown

To find  
 • The perimeter of triangular region PQR
 o For finding perimeter, we need to find the length of all the sides of PQR

Approach and Working out  
 Side PQ 
 • PQ^2 = 3^2 + 4^2 = 5^2
• PQ = 5 
Similarly, 
QR^2 = 1^2 + 7^2 = 50
 • QR = 5√2 
PR^2 = 3^2 + 4^2 = 5^2
 • PR = 5

Perimeter = 10 + 5√2

Thus, option E is the correct answer.
  Correct Answer: Option E

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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

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