Question: Rectangle’s height

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Hi Brent,
Please help me with the solution to this question.

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
gmat-admin's picture

This is more of a counting question than a geometry question. That said, it's a question I've answered many times on the Beat The GMAT forum.

My detailed solution can be found here: http://www.beatthegmat.com/og-228-t284238.html

Hey thanks for all your help so far!

For this I made a ratio of a smaller triangle with sides then multipled to get the height
smaller triangle sides = 1, 2, sq(5)
multiply ratio
sq(60)*(2/sq(5)) = x
x = 4sq(3)

Does this way always work as well?

gmat-admin's picture

Nice!
That approach will work for all analogous questions.

Cheers,
Brent

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