Back To Back Right Triangles - 2

Geometry Level 4

In the above figure, $ABD$ and $ACD$ are integer-length, right-angled triangles with the right angle at $D$ . If $AD = 12$ and $BD$ and $DC$ have different lengths, how many possible different lengths are there for $BC$ ?

Thanks to Brian for correcting my previous problem

3 1 0 6

1 solution

展豪張
Mar 6, 2016

We have:
$12^2+5^2=13^2$
$12^2+9^2=15^2$
$12^2+16^2=20^2$
$12^2+35^2=37^2$
$BD$ and $DC$ can be $5, 9, 16$ or $35$
The answer is $\binom 4 2=6$

Back To Back Right Triangles - 2

1 solution

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