Question

Сумма длин диагоналей ромба равна 14, а разность их длинравна 2. Найти площадь ромба.

Answer 1

х+у=14

х-у=2

х=2+у

2у+у=14

у=6

х=8

Ответ: 24

Answer 2

Sромба=АС*ВД/2, где АС И ВД - диагонали

АС=а, ВД=в

а=14-в

а-в=2

14-в-в=2

-2в=2-14

в=6

а=14-6=8

S=6*8/2=24 

 

Answer 3

Finding the Lengths of the Diagonals

To find the area of a rhombus, we first need to find the lengths of its diagonals. The problem states that the sum of the lengths of the diagonals is 14, and the difference between their lengths is 2.

Let's assume that the lengths of the diagonals are represented by variables d1 and d2. According to the given information, we can set up the following equations:

1. The sum of the lengths of the diagonals is 14: d1 + d2 = 14. 2. The difference between their lengths is 2: d1 - d2 = 2.

We can solve this system of equations to find the lengths of the diagonals.

Solving the System of Equations

To solve the system of equations, we can use the method of substitution or elimination. Let's use the method of elimination:

1. Add the two equations together to eliminate the variable d2: - (d1 + d2) + (d1 - d2) = 14 + 2 - Simplifying the equation: 2d1 = 16 - Dividing both sides by 2: d1 = 8.

2. Substitute the value of d1 into one of the original equations to find d2: - 8 + d2 = 14 - Subtracting 8 from both sides: d2 = 6.

Therefore, the lengths of the diagonals are d1 = 8 and d2 = 6.

Finding the Area of the Rhombus

The area of a rhombus can be calculated using the formula: Area = (d1 * d2) / 2, where d1 and d2 are the lengths of the diagonals.

Substituting the values we found, we get:

Area = (8 * 6) / 2 = 48 / 2 = 24.

Therefore, the area of the rhombus is 24 square units.

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