In the rectangle ABCD, the diagonals intersect at the point O, AB = 6 cm, AC = 13 cm, find the perimeter of the COD triangle.

A rectangle is a quadrangle in which all angles are right and equal to each other.

Since the opposite sides of the rectangle are equal, then AB = CD = 6 cm; BC = AD = 13cm.

The diagonals of the rectangle are equal and the intersection point is halved.

According to this: AC = BD;

AO = BO = OC = OD = AC / 2.

Consider a triangle ΔАСD. The triangle is rectangular since the angle ∠СDА = 90 °. In order to calculate the length of the AC diagonal, we use the Pythagorean theorem, according to which: The square of the hypotenuse is equal to the sum of the squares of the legs:

AC ^ 2 = CD ^ 2 + AD ^ 2;

AC ^ 2 = 6 ^ 2 + 13 ^ 2 = 36 + 169 = 205

AC = √205 = 14.32 cm;

AO = BO = OC = OD = 14.32 / 2 = 7.16 cm.

The perimeter of a triangle is the sum of all its sides:

P = CO + OD + CD;

P = 6 + 7.16 + 7.16 = 20.32 cm.

Answer: The perimeter of the triangle ΔCOD is 20.32 cm.