Question

Огородный участок, имеющий форму прямоугольника, одна сторона которого на 20м больше другой, требуется обнести изгородью. Определите длину изгороди, если известно, что площадь участка равна 8000м2.

Answer 1

Пусть одна сторона прямоугольника равна x, тогда другая сторона равна x+20
8000=x (x+20)
8000=x^2+20x
x^2+20x-8000=0
D=20^2-(-8000)×4=400+32000=32400=180^2
x=(-20+180)/2=160/2=80 или x=(-20-180)/2=-200/2=-100 - не подходит, т.к. длина не может быть отрицательно
x=80
длина изгороди=периметру прямоугольного участка=(x+(x+20))×2=(2x+20)×2=(2×80+20)×2=(160+20)×2=180×2=360 (м)
Ответ: 360м

Answer 2

Problem Analysis

We are given a rectangular garden plot with one side that is 20 meters longer than the other side. The area of the plot is known to be 8000 square meters. We need to determine the length of the fence required to enclose the garden.

Solution

Let's assume the shorter side of the rectangular garden plot is x meters. According to the problem statement, the longer side is 20 meters longer than the shorter side, so the longer side will be x + 20 meters.

The area of a rectangle is given by the formula: Area = length × width. In this case, the area is known to be 8000 square meters. Therefore, we can write the equation:

x × (x + 20) = 8000

To solve this equation, we can expand it and rearrange the terms:

x^2 + 20x - 8000 = 0

Now we can solve this quadratic equation to find the value of x. We can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this equation, a is the coefficient of x^2, b is the coefficient of x, and c is the constant term.

Comparing the equation x^2 + 20x - 8000 = 0 with the quadratic formula, we can see that a = 1, b = 20, and c = -8000.

Now we can substitute these values into the quadratic formula to find the possible values of x.