The legs of the rectangle are 40cm and 42cm by how much the radius of the inscribed

The legs of the rectangle are 40cm and 42cm by how much the radius of the inscribed circle is greater than the radius of the inscribed circle.

Using the Pythagorean theorem, we find the hypotenuse of a given right-angled triangle:

√ (40 ^ 2 + 42 ^ 2) = √ (1600 + 1764) = √3364 = 58.

Since the radius of the circumscribed circle of any right-angled triangle is equal to half of the hypotenuse of this triangle, the radius of the circumscribed circle of this triangle is 58/2 = 29 cm.

Let r denote the radius of the circle inscribed in this triangle.

Using the formula for the area of ​​a triangle in terms of the radius of the inscribed circle, we can compose the following equation:

40 * 42/2 = r * (40 + 42 + 58) / 2

solving which, we get:

40 * 21 = r * 140/2;

40 * 21 = r * 70;

r = 40 * 21/70 = 4 * 21/7 = 4 * 3 = 12 cm.

Find how much the radius of the inscribed circle is greater than the radius of the inscribed circle:

29 – 12 = 17 cm.

Answer: 17 cm.