Question

Длина школьного стадиона на 40 с больше ,чем ширина .найдите длину и ширину стадиона ,если его площадь равна 4500 м2

Answer 1

Х м - ширина стадиона,
(х+40) м - длина стадиона
х(х+40)=4500
х²+40х-4500=0
D=40²-4·(-4500)=1600+18000=19600
х₁=(-40+√19600)/2=(-40+140)/2=50м - ширина стадиона
х₂=(-40-140)/2=-90 - не подходит по условию задачи
50+40=90 м - длина стадиона

Answer 2

Finding the Length and Width of the Stadium

To find the length and width of the stadium, we can use the given information that the area of the stadium is 4500 m² and the length is 40 m more than the width.

Let's assume the width of the stadium is x meters. Since the length is 40 meters more than the width, the length can be represented as x + 40 meters.

The formula for the area of a rectangle is Area = Length × Width. Substituting the given values, we have:

4500 = (x + 40) × x

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

4500 = x² + 40x

Now, we have a quadratic equation. To solve it, we can set it equal to zero:

x² + 40x - 4500 = 0

We can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. Let's use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

In this case, a = 1, b = 40, and c = -4500. Substituting these values into the quadratic formula, we get:

x = (-40 ± √(40² - 4(1)(-4500))) / (2(1))

Simplifying further:

x = (-40 ± √(1600 + 18000)) / 2

x = (-40 ± √(19600)) / 2

x = (-40 ± 140) / 2

Now, we have two possible values for the width of the stadium:

1. x = (-40 + 140) / 2 = 100 / 2 = 50 2. x = (-40 - 140) / 2 = -180 / 2 = -90

Since the width cannot be negative, we discard the second solution.

Therefore, the width of the stadium is 50 meters.

To find the length, we can substitute this value back into the equation:

Length = Width + 40 = 50 + 40 = 90 meters

So, the length of the stadium is 90 meters.

Therefore, the length and width of the stadium are 90 meters and 50 meters, respectively.