Question

In a right-angled triangle, the lengths of sides containing the right angle are 20 cm and 21 cm. What is the radius of the circumcircle of the triangle?

Answer 1

There is a right-angled triangle.

In question it is given that the lengths of sides containing the right angle are 20 cm and 21 cm.

Suppose Perpendicular = 20 cm

Base = 21 cm

Hypotenuse = ?

Then, (Hypotenuse)² = (Perpendicular)² + (Base)²

(Hypotenuse)² = (20)² + (21)²

(Hypotenuse)² = 400 + 441

(Hypotenuse)² = 841

Hypotenuse = `sqrt(841)`

Hypotenuse = 29 cm

According to the theorem the radius of a circumcircle of a right-angled triangle is equals to the half of the hypotenuse of the triangle.

Hence, the radius = `29/2` cm = 14.5 cm.