Question

Стороны ромба равны 6, а его площадь 24. найти радиус вписанной окружности

Answer 1

Если площадь 24 то ее стороны равны 6 соответсвенно.Радиус может быть половина ее диагонали

Answer 2

R=S/p
S — площадь ромба, p — его полупериметр (p=2a, где a — сторона ромба).
r=24/12=2
p=6*2=12

Answer 3

Finding the Radius of the Inscribed Circle in a Rhombus

To find the radius of the inscribed circle in a rhombus with sides of 6 units and an area of 24 square units, we can use the following formula:

Radius of inscribed circle (r) = Area of the rhombus / Semiperimeter of the rhombus

Calculating the Semiperimeter of the Rhombus

The semiperimeter of a rhombus can be calculated using the formula: Semiperimeter = (Sum of all sides) / 2

Given that the sides of the rhombus are equal to 6 units, the sum of all sides is: Sum of all sides = 6 + 6 + 6 + 6 = 24 units

Therefore, the semiperimeter of the rhombus is: Semiperimeter = 24 / 2 = 12 units

Calculating the Radius of the Inscribed Circle

Now, we can calculate the radius of the inscribed circle using the formula mentioned earlier: Radius of inscribed circle (r) = Area of the rhombus / Semiperimeter of the rhombus

Given that the area of the rhombus is 24 square units, we can substitute these values into the formula: Radius of inscribed circle (r) = 24 / 12 = 2 units

Therefore, the radius of the inscribed circle in the rhombus is 2 units.