Question

Диагональ прямоугольника равна 13 см, а одна из сторон- 5 см. Найдите площадь и периметр прямоугольника. Желательно с рисунком Заранее спасибо!)

Answer 1

S=5 * а, где 5см -длина одной стороны,
               а -длина второй стороны.
13*13 =5*5 + а  выражаем а
а =√169-25=12см
S=5 * 12=60см
Рпр=2 * (а + в) , где а, в -стороны прямоугольника,
Рпр=2 *(12см + 5см) = 34см  

Answer 2

Calculation of the Area and Perimeter of a Rectangle

To find the area and perimeter of a rectangle, we need to know the length of its sides. In this case, we are given that the diagonal of the rectangle is 13 cm and one of the sides is 5 cm.

Let's denote the length of the rectangle as a and the width as b.

Using the Pythagorean theorem, we can relate the diagonal, length, and width of the rectangle:

a^2 + b^2 = diagonal^2

Substituting the given values, we have:

5^2 + b^2 = 13^2

Simplifying the equation, we get:

25 + b^2 = 169

Subtracting 25 from both sides, we have:

b^2 = 144

Taking the square root of both sides, we find:

b = 12

Now that we know the width of the rectangle, we can calculate its area and perimeter.

Calculation of the Area

The area of a rectangle is given by the formula:

Area = length * width

Substituting the given values, we have:

Area = 5 cm * 12 cm = 60 cm^2

Therefore, the area of the rectangle is 60 square centimeters.

Calculation of the Perimeter

The perimeter of a rectangle is given by the formula:

Perimeter = 2 * (length + width)

Substituting the given values, we have:

Perimeter = 2 * (5 cm + 12 cm) = 2 * 17 cm = 34 cm

Therefore, the perimeter of the rectangle is 34 centimeters.

Diagram

Here is a diagram to help visualize the rectangle:

     5 cm
+----------+
|          |
|          |
|          |
|          |
|          |
+----------+
     12 cm

I hope this helps! Let me know if you have any further questions.