Question

Площадь прямоугольника равна 40 см квадратных а его периметр равен 26 см чему равна длина и ширина прямоугольника???

Answer 1

Xy=40, 2x+2y=26, разделим второе уравнение на 2, выразим икси подставим в первое: (13-y)y=40, решим и получим корни 5 и 8

Answer 2

Длина 8 , а ширина 5

Answer 3

Problem Analysis

We are given that the area of a rectangle is 40 square centimeters and its perimeter is 26 centimeters. We need to find the length and width of the rectangle.

Solution

Let's assume the length of the rectangle is L and the width is W.

We know that the area of a rectangle is given by the formula: Area = Length * Width. So, we have the equation: L * W = 40.

We also know that the perimeter of a rectangle is given by the formula: Perimeter = 2 * (Length + Width). So, we have the equation: 2 * (L + W) = 26.

We can solve these two equations simultaneously to find the values of L and W.

Solving the Equations

Let's solve the equations using the given information.

From the equation L * W = 40, we can express L in terms of W as: L = 40 / W.

Substituting this value of L into the equation 2 * (L + W) = 26, we get: 2 * (40 / W + W) = 26.

Simplifying this equation, we get: 80 / W + 2W = 26.

Multiplying both sides of the equation by W, we get: 80 + 2W^2 = 26W.

Rearranging the equation, we get: 2W^2 - 26W + 80 = 0.

Now, we can solve this quadratic equation to find the values of W.

Using the quadratic formula, we have: W = (-b ± √(b^2 - 4ac)) / (2a).

For our equation 2W^2 - 26W + 80 = 0, the values of a, b, and c are: a = 2, b = -26, and c = 80.

Substituting these values into the quadratic formula, we get: W = (-(-26) ± √((-26)^2 - 4 * 2 * 80)) / (2 * 2).

Simplifying this equation, we get: W = (26 ± √(676 - 640)) / 4.

Simplifying further, we get: W = (26 ± √36) / 4.

Taking the square root of 36, we get: W = (26 ± 6) / 4.

So, we have two possible values for W: 1. W = (26 + 6) / 4 = 32 / 4 = 8. 2. W = (26 - 6) / 4 = 20 / 4 = 5.

Now, let's substitute these values of W back into the equation L * W = 40 to find the corresponding values of L.

For W = 8, we have: L * 8 = 40. Simplifying this equation, we get: L = 40 / 8 = 5.

For W = 5, we have: L * 5 = 40. Simplifying this equation, we get: L = 40 / 5 = 8.

Therefore, the length and width of the rectangle can be either 5 cm and 8 cm or 8 cm and 5 cm.

Answer

The length and width of the rectangle can be either 5 cm and 8 cm or 8 cm and 5 cm.