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Fun one... Right triangle PQR is to be constructed in the

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Fun one... Right triangle PQR is to be constructed in the [#permalink] New post 29 Sep 2005, 22:32
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Fun one...

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
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 [#permalink] New post 30 Sep 2005, 00:43
I pick C)9900


We have 10 possibilities for x and 11 for y.

We can proceed by first determining the right angle's vertex and then the length of the legs.

For the vertex, we have 11*10 possibilities.
For the legths we have:
horizontal: 9 possibilities
vertical: 10 possibilities.

Thus 11*10*10*9=9900
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 [#permalink] New post 30 Sep 2005, 09:03
C.

x co-ordinates count = 5 - (-4) + 1 = 10 {-4 <= x <= 5}
y co-ordinates count = 16 - 6 + 1 = 11

all combinations for P: 10 * 11
all combinations for R: 9 * 1 (y remains same as that of P as PR is parallel to x-axis)
all combinations for Q: 1 * 10 (x same as P. y other than what is selected for P or R)

total combinations : 10 * 11 * 9 * 1 * 1 * 10 = 9900

the problem becomes simple if you draw tringle on paper.
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 [#permalink] New post 30 Sep 2005, 09:24
Got C, P and q should have same y value and P and R should have same x vaue so

11*10*9*10 = 9900
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  [#permalink] 30 Sep 2005, 09:24
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