Right triangle PQR is to be constructed

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?

2 Explanations

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Imran Manji

I broke this problem down by different points:

Level set: there are 10 options for X and 11 options for Y

Point P: There are a total of 110 options (10 x 11)
Point R: Since the Y value will stay the same, we have 9 options for X (-1 because a point is already taken for P)
Point Q: Since the X value will stay the same, we have 10 options for Y (-1 because a point is already taken for Q)

110 x 10 x 9 = 9,900

Is my logic correct?

Apr 26, 2016 • Comment

Cydney Seigerman, Magoosh Tutor

Hi Imran!

Yes, that is a great way to approach this problem! Good job :)

Apr 30, 2016 • Reply

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Mike McGarry, Magoosh Tutor