Question

Знайдіть площу ромба сторона якого дорівнює 10 см а різниця діагоналей 4 см​

Answer 1

АС - більша діагональ, ВД - менша.
АС - ВД = 10см
Нехай ВД = х см, АС = 10 + х см
Діагоналі перетинаються під прямим кутом і діляться навпіл.
СО = ОА = (10 + х) / 2
ВО = ОД = х/2
Розглянемо трикутника ВСО:
він прямокутний кут О = 90градусів
Застосуємо теорему Піфагора:
ВС² = ВО² + СО²
25² = ((10 + х)/2)² + (х/2)²
625 = (100 + 20х + х²)/4 + х²/4
625 = (100 + 20х + 2х²) / 4
625 = (2 * (х² + 10х + 50)) / 4
625 = (х² + 10х + 50) / 2
1250 = х² + 10х + 50
х² + 10х - 1200 =0
шукай по дискрімінанту
Д = 70²
х1 = 30, х2 = -40
х2 = -40 -незадовільняє умову (довжина не може бути відємною)
Отже ВД = 30 см, АС = 30 + 10 = 40 см
S = 1/2 * АС * ВД = 1/2 * 30 * 40 = 600 см²

Answer 2

Finding the Area of a Rhombus

To find the area of a rhombus, we need to know the length of one of its sides and the difference between its diagonals. In this case, we are given that the side length is 10 cm and the difference between the diagonals is 4 cm.

Let's proceed with finding the area of the rhombus.

Formula for the Area of a Rhombus

The formula for finding the area of a rhombus is:

Area = (d1 * d2) / 2

Where: - d1 and d2 are the lengths of the diagonals of the rhombus.

Finding the Length of the Diagonals

To find the length of the diagonals, we can use the given information about the difference between the diagonals.

Let's assume that the lengths of the diagonals are d1 and d2, where d1 is the longer diagonal.

We know that the difference between the diagonals is 4 cm. Therefore, we can write the following equation:

d1 - d2 = 4

Solving for the Diagonals

To solve for the diagonals, we need another equation. We can use the fact that the diagonals of a rhombus bisect each other at right angles.

Since the diagonals bisect each other, we can form two right triangles within the rhombus. The sides of these triangles are half the lengths of the diagonals.

Let's call half the length of d1 as x1 and half the length of d2 as x2.

We can write the following equations based on the right triangles:

x1^2 + (10/2)^2 = d1^2 x2^2 + (10/2)^2 = d2^2

Simplifying these equations, we get:

x1^2 + 25 = d1^2 x2^2 + 25 = d2^2

Substituting the Values

Now, let's substitute the values we have into the equations.

We know that the side length is 10 cm, so the length of half the side is 5 cm.

Substituting this value into the equations, we get:

x1^2 + 25 = d1^2 x2^2 + 25 = d2^2

5^2 + 25 = d1^2 5^2 + 25 = d2^2

Simplifying further, we get:

25 + 25 = d1^2 25 + 25 = d2^2

50 = d1^2 50 = d2^2

Taking the square root of both sides, we find:

d1 = sqrt(50) d2 = sqrt(50)

Simplifying, we get:

d1 = 5 * sqrt(2) d2 = 5 * sqrt(2)

Calculating the Area

Now that we have the lengths of the diagonals, we can calculate the area of the rhombus using the formula:

Area = (d1 * d2) / 2

Substituting the values, we get:

Area = (5 * sqrt(2) * 5 * sqrt(2)) / 2

Simplifying, we get:

Area = (25 * 2) / 2

Area = 25

Therefore, the area of the rhombus is 25 square centimeters.

Please note that the calculations above are based on the given information and assumptions. If there are any additional details or constraints, the answer may vary.