Question

Диагонали ромба равны 16 и 30 см. Найти высоту ромба.

Answer 1

площадь ромба 1/2*16*30=240. 

Сторона ромба - гипотенуза треугольника с катетами 1/2*16=8 и 1/2*30=15, т.е. гипотенуза равна корень квадратный из 8*8+15*15=64+225=289 или это 17.

Площадь через стоорну и высоту: 240=н*17  н=240:17=14 целых 2/17

Answer 2

Finding the Height of a Rhombus

To find the height of a rhombus, we can use the formula:

Area = (diagonal1 * diagonal2) / 2

Given that the diagonals of the rhombus are 16 cm and 30 cm, we can substitute these values into the formula to find the area of the rhombus.

Area = (16 cm * 30 cm) / 2

Calculating this, we get:

Area = 240 cm² The area of a rhombus can also be calculated using the formula:

Area = (base * height) / 2

Since the base of a rhombus is equal to one of its sides, we can rewrite the formula as:

Area = (side * height) / 2

We can rearrange this formula to solve for the height:

Height = (2 * Area) / side

In this case, since we know the area of the rhombus is 240 cm², and the side length is unknown, we need to find the side length first.

To find the side length, we can use the formula:

Side = √((diagonal1/2)² + (diagonal2/2)²)

Substituting the given values:

Side = √((16 cm/2)² + (30 cm/2)²)

Calculating this, we get:

Side = √(8² + 15²) = √(64 + 225) = √289 = 17 cm Now that we know the side length is 17 cm, we can substitute this value into the formula to find the height:

Height = (2 * 240 cm²) / 17 cm

Calculating this, we get:

Height ≈ 28.24 cm

Therefore, the height of the rhombus is approximately 28.24 cm.

Answer:

The height of the rhombus is approximately 28.24 cm.