In the square ABCD, BD = 12 cm, the point of intersection of the diagonals O, AB = 16 cm Find the perimeter of the triangle BOA.

Since ABCD is a square, triangle ABC is rectangular, in which, according to the Pythagorean theorem, we determine the length of the hypotenuse AC.

AC ^ 2 = AB ^ 2 + BC ^ 2 = 256 + 256 = 512.

AC = √512 = 16 * √2 cm.

The diagonals of the square are equal and at the point of intersection, they are divided in half, then ВD = АС = 16 * √2 cm, ОВ = AO = 16 * √2 / 2 = 8 * √2 cm.

Then Pvoa = AB + OB + AO = 16 + 8 * √2 + 8 * √2 = 16 + 16 * √2 = 16 * (1 + √2) cm.

Answer: The perimeter of the BOA triangle is 16 * (1 + √2) cm.