Question

Периметр прямоугольника равен 28м а его площадь равна 40м квадратных найдите стороны прямоугольника

Answer 1

Длина 10
ширина 4
10*4=40
10+10+4+4=28

Answer 2

Problem Analysis

We are given that the perimeter of a rectangle is 28m and its area is 40 square meters. We need to find the sides of the rectangle.

Solution

Let's assume the length of the rectangle is a and the width is b.

The perimeter of a rectangle is given by the formula: P = 2(a + b). The area of a rectangle is given by the formula: A = a * b.

We are given that the perimeter is 28m, so we have the equation: 28 = 2(a + b). We are also given that the area is 40 square meters, so we have the equation: 40 = a * b.

We can solve these two equations simultaneously to find the values of a and b.

Solving the Equations

Let's solve the equations using the given information.

From the equation 28 = 2(a + b), we can simplify it to a + b = 14.

From the equation 40 = a * b, we can rewrite it as b = 40 / a.

Substituting the value of b in the equation a + b = 14, we get a + (40 / a) = 14.

To solve this equation, we can multiply through by a to eliminate the fraction: a^2 + 40 = 14a.

Rearranging the equation, we get a^2 - 14a + 40 = 0.

Factoring the quadratic equation, we get (a - 10)(a - 4) = 0.

So, a = 10 or a = 4.

If a = 10, then b = 40 / 10 = 4. If a = 4, then b = 40 / 4 = 10.

Therefore, the sides of the rectangle can be either 10m and 4m or 4m and 10m.

Answer

The sides of the rectangle can be either 10m and 4m or 4m and 10m.