Question

Найдите сторону ромба , площадь которого равна 12 см в квадрате , а высота - 2,4 см.

Answer 1

S=a*h
12=а*2,4
а=12:2,4
а=5

Answer 2

Finding the Side of a Rhombus with Given Area and Height

To find the side of a rhombus when the area and height are given, we can use the formula for the area of a rhombus:

Area of a Rhombus = (1/2) * (diagonal1) * (diagonal2)

Since the diagonals of a rhombus are perpendicular bisectors of each other, we can use the height and one of the diagonals to find the area and then calculate the side length.

Let's use the given information: the area of the rhombus is 12 cm², and the height is 2.4 cm.

Calculation:

1. We know that the area of the rhombus is given by the formula: Area = (1/2) * (diagonal1) * (diagonal2).

2. Since the diagonals of a rhombus are perpendicular bisectors of each other, we can use the height and one of the diagonals to find the area.

3. Let's assume the height of the rhombus is the perpendicular distance between the two diagonals.

4. We can use the formula for the area of a rhombus to find the length of the other diagonal.

Area = (1/2) * (diagonal1) * (height)

Substituting the given values:

12 = (1/2) * (diagonal1) * 2.4

Solving for diagonal1:

diagonal1 = (12 * 2) / 2.4 = 10 cm

5. Now that we have the length of one diagonal (diagonal1), we can use it to find the side length of the rhombus.

In a rhombus, the diagonals bisect each other at right angles, forming four congruent right-angled triangles.

The side length of the rhombus is the hypotenuse of one of these right-angled triangles.

Using the Pythagorean theorem, we can find the side length:

Side length = √(height² + (diagonal1/2)²)

Substituting the given values:

Side length = √(2.4² + (10/2)²) = √(5.76 + 25) = √30.76 ≈ 5.54 cm

Answer:

The side length of the rhombus is approximately 5.54 cm.

Please note that the calculations are based on the assumption that the height is the perpendicular distance between the diagonals. If there are any additional specifications or assumptions, please let me know, and I'll be happy to assist you further.