Question

Газон прямоугольной формы обнесён бордюром, длина которого 40 м. Площадь газона 96 м2. Найдите стороны газона.

Answer 1

Пусть стороны газона равны x и y. Из условия составим систему уравнений

$\displaystyle \left \{ {{2(x+y)=40} \atop {xy=96}} \right. \Rightarrow~~~ \left \{ {{x+y=20} \atop {xy=96}} \right.$
Из первого уравнения выразим переменную х: x = 20-y и подставим во второе уравнение

$y(20-y)=96\\ y^2-20y+96=0\\ (y-10)^2-4=0\\ y-10=\pm 2\\ y_1=12\\ y_2=8\\ \\ x_1=20-12=8\\ x_2=20-8=12$

Answer 2

Calculation of the sides of the rectangular lawn

To find the sides of the rectangular lawn, we can use the formula for the area of a rectangle: Area = Length x Width.

Given that the length of the lawn is 40 meters and the area is 96 square meters, we can substitute these values into the formula and solve for the width.

Let's denote the width of the lawn as w.

The formula becomes:

96 = 40 x w

To find the value of w, we can divide both sides of the equation by 40:

w = 96 / 40

Simplifying the right side of the equation gives us:

w = 2.4

Therefore, the width of the rectangular lawn is 2.4 meters.

To summarize: - The length of the rectangular lawn is 40 meters. - The width of the rectangular lawn is 2.4 meters.