Question

Отношение диагоналей ромба равно 6:23, а сумма длин данных элементов — 29 см. Чему равны диагонали и площадь ромба? (Запиши без единиц измерения.)Длина меньшей диагонали: см.Длина большей диагонали: см.Площадь ромба: см2​

Answer 1

Ответ:

Пусть деагонали будут 6х и 23х тогда:

6х + 23х = 29

29х = 29

х = 1(см)

Соответственно

6х =6см

23х =23см

Длина меньшей диагонали: 6 см.

Длина большей диагонали: 23 см.

S=1/2×6×23= 69

Площадь ромба: 69 см2

Answer 2

Relationship between diagonals of a rhombus

The relationship between the diagonals of a rhombus can be determined using the given information. The ratio of the diagonals is given as 6:23, and the sum of their lengths is 29 cm.

Let's denote the length of the smaller diagonal as x and the length of the larger diagonal as y.

We can set up the following equations based on the given information:

1. The ratio of the diagonals: x:y = 6:23 2. The sum of their lengths: x + y = 29 cm

To find the lengths of the diagonals, we can solve these equations simultaneously.

Solving for the lengths of the diagonals

To solve the equations, we can use the method of substitution. We can rearrange the first equation to express x in terms of y:

x = (6/23) * y

Substituting this value of x into the second equation, we get:

(6/23) * y + y = 29 cm

Simplifying the equation:

(29/23) * y = 29 cm

Dividing both sides of the equation by (29/23), we find:

y = 23 cm

Substituting this value of y back into the first equation, we can find x:

x = (6/23) * 23 cm = 6 cm

Therefore, the length of the smaller diagonal is 6 cm and the length of the larger diagonal is 23 cm.

Calculating the area of the rhombus

The area of a rhombus can be calculated using the formula:

Area = (1/2) * d1 * d2

where d1 and d2 are the lengths of the diagonals.

Substituting the values we found earlier, we get:

Area = (1/2) * 6 cm * 23 cm = 69 cm^2

Therefore, the area of the rhombus is 69 cm^2.

To summarize: - Length of the smaller diagonal: 6 cm - Length of the larger diagonal: 23 cm - Area of the rhombus: 69 cm^2