Question

Lан прямоугольник у которого длина в три раза больше ширины Известно что периметр прямоугольника численно равен его площади Найдите стороны прямоугольнгика

Answer 1

Ответ:длина 8/3 ширина 8/9

Объяснение:

а=3b, где а-длина, а ширина это b

P=2(a+b)=2*4a

S=a*3a=3a^2

P=S

8a=3a^2

сократим на а

8=3а

а=8/3

b=a/3=(8/3)/3=8/9

Answer 2

Problem Analysis

We are given that the length of a rectangle is three times its width. We also know that the perimeter of the rectangle is numerically equal to its area. We need to find the dimensions of the rectangle.

Solution

Let's assume that the width of the rectangle is x. According to the problem, the length of the rectangle is three times its width, so the length would be 3x.

The perimeter of a rectangle is given by the formula: 2 * (length + width). The area of a rectangle is given by the formula: length * width.

According to the problem, the perimeter of the rectangle is numerically equal to its area. Therefore, we can set up the following equation:

2 * (3x + x) = 3x * x

Simplifying the equation, we get:

8x = 3x^2

Rearranging the equation, we get:

3x^2 - 8x = 0

Factoring out an x, we get:

x(3x - 8) = 0

Setting each factor equal to zero, we get two possible solutions:

1. x = 0 2. 3x - 8 = 0

Since the width of a rectangle cannot be zero, we can ignore the first solution. Solving the second equation for x, we get:

3x - 8 = 0 3x = 8 x = 8/3

So, the width of the rectangle is 8/3 and the length is 3 * (8/3) = 8.

Therefore, the sides of the rectangle are 8/3 and 8.

Answer

The sides of the rectangle are 8/3 and 8.