452. The sum of the three sides of a right-angled triangle is 156 meters. The area is 1014 square meters. Find the sides.

## Garnier Problems.
452. We have:

$$
\begin{gathered}
x+y+z=156 \\
xy=2028 \\
z^{2}=x^{2}+y^{2}
\end{gathered}
$$

from which

$$
(x+y)^{2}=x^{2}+y^{2}+2xy=z^{2}+4056=(156-z)^{2}
$$

or

$$
4056=156^{2}-312z
$$

from which

$$
z=65
$$

therefore,

$$
x+y=91
$$

By the sum and product, we find:

$$
x=39 ; y=52
$$

Garnier, Jean Guillaume (1766-1840), French mathematician, educator, professor at the École Polytechnique, author of a number of courses on elementary and higher mathematics. His "Éléments de géométrie" was published in 1813.