Question

Высота ромба на 1.8 см меньше, чем его сторона. периметр равен 48 см. Найти площадь.

Answer 1

Сторона а = х
сторона b = x+1.8
P= 48
S = ? см
Решение:
1) (х+х+1.8) * 2 = 48
     (2х+1.8) = 48:2
     (2х + 1.8) = 24
     2х = 24 - 1.8 
     2X = 22.2
       х = 11.1 - сторона а.
2) 11.1+1.8 = 12.9 - сторона b
3) 11.1 * 12.9 = 143.19 см в кв. - S 
Ответ: S = 143 см в кв.

Answer 2

Problem Analysis

We are given that the height of a rhombus is 1.8 cm less than its side length, and the perimeter of the rhombus is 48 cm. We need to find the area of the rhombus.

Solution

To find the area of the rhombus, we need to know the length of its side. Let's assume the side length of the rhombus is x cm.

From the given information, we know that the height of the rhombus is 1.8 cm less than its side length. So, the height can be expressed as x - 1.8 cm.

The perimeter of a rhombus is given by the formula: 4 * side length. In this case, the perimeter is 48 cm. So, we can write the equation:

4x = 48

Simplifying the equation, we find:

x = 12

Now that we know the side length of the rhombus is 12 cm, we can find the area of the rhombus using the formula: area = (diagonal1 * diagonal2) / 2.

In a rhombus, the diagonals are perpendicular bisectors of each other, dividing the rhombus into four congruent right-angled triangles. The length of each diagonal can be found using the Pythagorean theorem.

Let's label the diagonals as d1 and d2. The length of each diagonal can be expressed as:

d1 = √(x^2 + (x - 1.8)^2) d2 = √(x^2 + (x - 1.8)^2)

Substituting the value of x as 12, we can calculate the length of each diagonal.

Finally, we can calculate the area of the rhombus using the formula mentioned earlier.

Calculation

Let's calculate the area of the rhombus step by step.

1. Calculate the length of each diagonal: - d1 = √(12^2 + (12 - 1.8)^2) - d2 = √(12^2 + (12 - 1.8)^2)

2. Calculate the area of the rhombus: - area = (d1 * d2) / 2

Answer

The area of the rhombus is approximately .