The diagonals of the rhombus are 30-40 cm. Find the radius of the circle inscribed in the rhombus.

It is known from the condition that the diagonals of the rhombus are equal to 30 and 40 cm, respectively. And we need to find the radius of the circle inscribed in the rhombus.

So, let R be the radius of the circle.

Let’s apply the formula:

R = (d1 * d2): 4a, where a is the side of the rhombus, and d1 and d2 are its diagonals.

First of all, we need to find the side of the diamond. For this we apply the Pythagorean theorem to the triangle formed by the halves of the diagonals and the side of the rhombus.

The side of the rhombus is the hypotenuse, half of the diagonals are the legs.

a ^ 2 = b ^ 2 + c ^ 2;

a ^ 2 = (30/2) ^ 2 + (40/2) ^ 2;

a = √ (15 ^ 2 + 20 ^ 2) = √ (225 + 400) = √625 = 25.

We substitute the values ​​into the formula and perform the calculations:

R = (40 * 30): (4 * 25) = 1200: 100 = 12 cm.