A circle with a radius of 6.5 cm is described around the rectangle ABCD.

A circle with a radius of 6.5 cm is described around the rectangle ABCD. Find the perimeter of the rectangle if one of its sides is 5cm.

Since a circle is circumscribed around the rectangle, point O, the intersection point of the diagonals of the rectangle, is the center of the circumscribed circle.

Then AC = BD = 2 * R = 2 * 6.5 cm = 13 cm.

In a right-angled triangle ABD, according to the Pythagorean theorem, we determine the length of the leg AD.

AD ^ 2 = BD ^ 2 – AB ^ 2 = 169 – 25 = 144.

AD = 12 cm.

Let’s define the perimeter of the rectangle ABCD.

Ravsd = 2 * (AB + AD) = 2 * (5 + 12) = 34 cm.

Answer: The perimeter of the rectangle is 34 cm.