The legs of a right-angled triangle are 3 cm and 4 cm. Parallel to the hypotenuse, a straight line is drawn

The legs of a right-angled triangle are 3 cm and 4 cm. Parallel to the hypotenuse, a straight line is drawn, which divides this triangle into two parts equal in area. Find the perimeter of the smaller triangle

The area of the original triangle is S = 3 * 4/2 = 6 cm ^ 2.
Its hypotenuse: c = √ (3 ^ 2 + 4 ^ 2) = 5 cm.
Area of the smaller triangle: 6 cm ^ 2/2 = 3 cm ^ 2.
The sharp angles of the truncated triangle will be the same as those of the original one (the hypotenuse and the straight line are parallel, and the pairs of angles are one-sided corresponding). Hence, the large and small triangles are similar. Let the sides of a small triangle be k times less.
Small triangle area:
((3 / k) * (4 / k)) / 2 = 3 cm ^ 2;
12 / k ^ 2 = 6 cm ^ 2;
k = √2.
Small triangle perimeter:
p = 3 / √2 + 4 / √2 + 5 / √2 = 12 / √2 cm.
Answer: 12 / √2 cm.