how many triangles?

shipra · Posted: Sun Jun 29, 2008 2:52 am Post subject: how many triangles?

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

A. 110
B. 1100
C. 9900
D. 10000
E. 12100

simpdimp · Posted: Mon Jun 30, 2008 6:01 pm Post subject: how many triangles?

X coordinate has 10 possible values between -4 and 5
Y coordinate has 11 possible values between 6 and 16

1. Fix P first, P can have 10 values across X axis and 11 across Y axis. So, that's 11*10 = 110

2. Since PR is parallel to X axis, R is on the same line as P. So, R has 9 (10-1) values left along X axis. So far 110*9 = 990

3. Since PQR is a right angle triangle and the right angle is at P, PQ is parallel to Y axis. So, Q has 10 (11-1) values left. So, 990*10 = 9900

The answer is C - 9900

shipra · Posted: Mon Jun 30, 2008 11:04 pm Post subject:

Thanx a lot...
really helped...

rabab · Posted: Sat Oct 18, 2008 7:36 am Post subject: Re: how many triangles?

cmoney · Posted: Sun Oct 19, 2008 11:46 am Post subject:

I think that the point is that to make a triangle, the the points need to exist on different values. An example would be a triangle where the base points are the same...this creates a line, so it's impossible. Sine R cannot have the same value as P, you have subtract one from the possible locations. (10-1).

I hope that helped. Anyone feel free to correct me if I'm wrong.