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How many triangles possible?

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by refreshment » Fri Feb 27, 2009 5:26 am
Right triange 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 1100
C 9900
D 10000
E 12100
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by BuckeyeT » Fri Feb 27, 2009 2:35 pm
What's the OA?

I'm getting a different value. But, I also might be setting up the problem incorrectly.
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by nitya34 » Fri Feb 27, 2009 9:15 pm
its 9*10*11
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by Uri » Sun Mar 01, 2009 12:33 pm
X coordinate has 10 possible values between -4 and 5
Y coordinate has 11 possible values between 6 and 16

P can have 10 values across X axis and 11 across Y axis. So, P can have a total of 11*10= 110 positions.

Since PR is parallel to X axis, R is on the same line as P. So, R has 10-1 = 9 values left along X axis.

Since PQR is a right angle triangle and the right angle is at P, PQ is parallel to Y axis. So, Q has 11-1 = 10 values left.

So, total number of possible triangles = 110 * 9 * 10 = 9900

Ans. (C)
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