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Right triangle PQR is to be constructed in the xy-plane so [#permalink]
13 Oct 2008, 02:13

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Difficulty:

65% (hard)

Question Stats:

64% (02:34) correct
36% (02:14) wrong based on 454 sessions

Right triangle PQR is to be constructed in the xy-plane so that the right angle is at P and PR is parallel to the x-axis. The x- and y-coordinates of P, Q, and R are to be integers that satisfy the inequalities -4 <= x <= 5 and 6<= y<= 16. How many different triangles with these properties could be constructed?

Re: PS : RIGHT TRIANGLE PQR [#permalink]
10 Dec 2010, 00:01

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abdullaiq wrote:

Could someone please explain how those numbers came out? Where did the 11, 10, and 9 came from? There is no specific point for them.

gettinit wrote:

yes can someone please explain in detail please? Thanks

Right triangle PQR is to be constructed in the xy-plane so that the right angle is at P and PR is parallel to the x-axis. The x and Y coordinates of P,Q and R are to be integers that satisfy the inequalitites -4≤ X≤ 5 and 6≤ y≤ 16. How many different triangles with these properties could be constructed? A. 110 B. 1100 C. 9900 D. 10000 E. 12100

We have the rectangle with dimensions 10*11 (10 horizontal dots and 11 vertical). PQ is parallel to y-axis and PR is parallel to x-axis.

Choose the (x,y) coordinates for vertex P (right angle): 10C1*11C1; Choose the x coordinate for vertex R (as y coordinate is fixed by A): 9C1, (10-1=9 as 1 horizontal dot is already occupied by A); Choose the y coordinate for vertex Q (as x coordinate is fixed by A): 10C1, (11-1=10 as 1 vertical dot is already occupied by A).

Right triangle PQR is to be constructed in the xy-plane so that the right angle is at P and PR is parallel to the x-axis. The x- and y-coordinates of P, Q, and R are to be integers that satisfy the inequalities -4 <= x <= 5 and 6<= y<= 16. How many different triangles with these properties could be constructed?

(A) 110 (B) 1,100 (C) 9,900 (D) 10,000 (E) 12,100

I just plotted 10 horizontal points and 11 vertical points and solved it using the following formula:

(11-1)*(10-1)*11*10 = 10*9*11*10=9900 Matched with Bunuel's approach and found the logic was pretty similar.

If you plot the points; you would see that you can make 90 right triangles at every point. Then, just multiply this figure with the total number of points.

Difficult Geometry Question [#permalink]
23 Aug 2011, 19:26

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Right triangle PQR is to be constructed in the xy-plane so that the right angle is at P and PR is parallel to the x-axis. The x- and y-coordinates of P,Q, and R are to be integers that satisfy the inequalities -4 is less than or equal to x which is less than or equal to 5 and 6 is less than or equal to y which is less than or equal to 16. How many different triangles with these properties could be constructed?

Re: Right triangle PQR is to be constructed in the xy-plane [#permalink]
03 Jul 2013, 11:44

Expert's post

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akijuneja wrote:

Right triangle PQR is to be constructed in the xy-plane so that the right angle is at Pand PR is parallel to the x-axis. The x- and y-coordinates of P, Q, and Rare to be integers that satisfy the inequalities -4 <= x =<5 and 6=<y =<16. How many different triangles with these properties could be constructed? (A) 110 (B) 1,100 (0 9,900 (D) 10,000 (E) 12,100

Merging topics. Please refer to the solutions above.

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