The height of a right-angled triangle divides it into triangles with perimeters p1 and p2. find the perimeter of the rectangle.

Let’s call a right-angled triangle ABC. The height of a triangle is the perpendicular dropped from its vertex to the opposite side. Let us drop the perpendicular from point B to line AC. The AC line is divided into two parts – AH, HC. The height BH divides ABC into two right-angled triangles – ABH and HBC. Let the perimeter of ABH be p1 and HBC – p2. Knowing the perimeters of the two triangles, we can find the perimeter of ABC. To do this, you need to fold them.

p (ABC) = p1 + p2.

Answer: p (ABC) = p1 + p2.