Given a rectangle ABCD. The CD side is 30 mm and the AD side is 1 cm longer than the CD side. The OA segment is 25 mm.

Given a rectangle ABCD. The CD side is 30 mm and the AD side is 1 cm longer than the CD side. The OA segment is 25 mm. What are the other elements of the rectangle ABCD?

It is known that the length of the CD side is 30 mm.

Let’s calculate what the length of the side AD is equal to:

1 cm = 10 mm.

AD = 30 + 10 = 40 mm.

In a rectangle, opposite sides are equal, therefore:

CD = AB = 30mm = 3cm.

AD = BC = 40 mm = 4 cm.

Let’s calculate the length of BD and OC:

BD = √ (3² + 4²) = √25 = 5 cm.

BD = AC = 50 mm;

OC = 50 – 25 = 25 mm.

Let’s calculate the perimeter of the rectangle:

P = 2 * (a + b) = 2 * (3 + 4) = 2 * 7 = 14 cm.

Answer: AB = 3 cm, BC = 4 cm, BD = 5 cm, OC = 25 mm, P = 14 cm.