# The base of a pyramid is a right triangle with

The base of a pyramid is a right triangle with the longest side = 12cm. All non base edges are also equal to 12cm. And how can I find the height of the pyramid?
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Corinne Choi
Use Thales' theorem.
You can select the points
$A=\left(-6,0,0\right),B=\left(+6,0,0\right),$
to form the longest side of the base triangle. The other point $C$ lies on a circle of which $AB$ is the diameter, as
${y}^{2}+\left[6-x{\right]}^{2}+{y}^{2}+\left[6+x{\right]}^{2}=144,$
so
${x}^{2}+{y}^{2}=36$
The top point $T$ is given by $\left(0,0,z\right)$ and it is clear that
$|AT|=|BT|=|CT|$
as $A$, $B$ and $C$ lie on the same circle, as $|AT|=|BT|=|AB|$, we obtain
$z=6\sqrt{3}$