A square is inscribed in a right-angled triangle with legs 3 and 5, which has a common right

A square is inscribed in a right-angled triangle with legs 3 and 5, which has a common right angle with the triangle. find the perimeter of the square.

Let the triangle ABC be given, the angle A is equal to 90º.
And the square AB1C1D is inscribed, point B1 lies on AB, point C1 lies on BC, point D lies on AC.
Triangles ABC and B1BC1 are similar, since angle A = B1, angle B is common, angle C = C1.
Let x be the side of the square.
AC = 5, AB = 3.
AB1 = B1C1 = C1D = AD = x.
From the similarity of triangles:
B1C1 / AC = B1B / AB.
Then,
x / 5 = (3 – x) / 3;
3 * x = 5 * (3 – x);
3 * x = 15 – 5 * x;
8 * x = 15;
x = 1.875.
The perimeter of the square is:
Pkv = 4 * x = 4 * 1.875 = 7.5.