Question

Укажите систему уравнений которая является математической моделью ситуации диагональ прямоугольника со сторонами х и у равна 26 а его периметр равен 68

Answer 1

{√(х² +у²)=26
{ 2*(х+у)=68

Answer 2

Диагональ в данном случае рассмотрим как гипотенузу  прямоугольного треугольника катеты которого равны сторонам соответствующего  прямоугольника
получим систему :

{√(х² +у²)=26
{ 2*(х+у)=68

Answer 3

Mathematical Model for the Diagonal of a Rectangle

To find the mathematical model for the situation described, we need to consider a rectangle with sides of length x and y. The diagonal of the rectangle is given as 26, and the perimeter is given as 68.

Let's denote the length of the rectangle as x and the width as y. The perimeter of a rectangle is given by the formula:

Perimeter = 2x + 2y In this case, the perimeter is given as 68. So we can write the equation:

2x + 2y = 68

The diagonal of a rectangle can be found using the Pythagorean theorem, which states that the square of the hypotenuse (diagonal) is equal to the sum of the squares of the other two sides. In this case, the diagonal is given as 26, so we can write the equation:

x^2 + y^2 = 26^2 Therefore, the system of equations that represents the mathematical model for the given situation is:

2x + 2y = 68 x^2 + y^2 = 26^2

These equations can be solved simultaneously to find the values of x and y that satisfy both equations and represent the sides of the rectangle.

Please note that the above equations are derived based on the information provided in the question and are not sourced from external references.