In the rectangle ABCD, the diagonals intersect at the point O, AB = 9 cm, AC = 16 cm

In the rectangle ABCD, the diagonals intersect at the point O, AB = 9 cm, AC = 16 cm. Find the perimeter of the COD triangle.

In a rectangle, the opposite sides are equal. This means that in the rectangle ABCD the sides AB and CD are equal, and the sides BC and AD are also equal.

CD = AB = 9 cm.

The COD triangle is formed by the side CD of the rectangle and the halves of the diagonals BC and BD.

OC = AC / 2; OD = BD / 2.

Let’s find OS and OD using the properties of the rectangle diagonals: 1) The rectangle diagonals are equal, 2) The rectangle diagonals intersect and the intersection point is halved.

OC = OD = AC / 2.

Find the diagonal AC by the Pythagorean theorem: The square of the hypotenuse is equal to the sum of the squares of the legs.

AC² = AB² + BC²;

AC² = 9² + 16² = 81 + 256 = 337;

AC = √337 (cm).

OS = OD = (√337) / 2

The perimeter of a triangle is equal to the sum of the lengths of its three sides.

P = OC + OD + CD;

P = (√337) / 2 + (√337) / 2 + 9 = 2 * (√337) / 2 + 9 = √337 + 9 (cm).

Answer. √337 + 9 cm.