* Edited with input from Graham Holmes and Philip Morris Jones.
I don’t believe it is possible to dissect a square into four Pythagorean triangles (a Pythagorean triangle is a right-angled triangle where all the sides are whole numbers). But there are some rectangles that are close to a square that can be so dissected.
Can you dissect each of these rectangles into four Pythagorean triangles?
168 x 169
252 x 253
272 x 273
One of these uses four identical triangles, one uses two pairs of identical triangles, and one uses four different triangles (although two of the triangles are similar).