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555-605 (Medium)|   Geometry|      
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Bunuel
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In the figure above, the grid consists of unit squares and P, Q and R 09 Aug 2017, 02:04
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25% (medium)

Question Stats:

79% (01:30) correct 21% (02:11) wrong based on 68 sessions

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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

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E
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In the figure above, the grid consists of unit squares and P, Q and R 09 Aug 2017, 02:11
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Bunuel

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

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

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

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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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In the figure above, the grid consists of unit squares and P, Q and R 31 Oct 2019, 05:46
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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 21 Aug 2024, 03:32
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