Question

бассейн имеет прямоугольную форму одна из его сторон на 6метров больше другой. Бассейн окружен дорожкой, ширина этой дорожки равна 0,5 метра, а площадь 15 метров.Чему равна площадь бассейна?

Answer 1

Сначала всё обозначим:
ширина бассейна по условию х; 
длина бассейна  х+6;ширина прямоугольника,в котором находится бассейн, х + 1 (добавилось по 0,5 м с каждой стороны за счёт дорожки);
длина этого же прямоугольника х + 7 (также добавилось по 0,5 м с двух сторон за счёт дорожки).
Дальше из площади большого прямоугольника вычитаем площадь малого(бассейн) и получаем разницу 15 кв.
метров - площадь всей дорожки по условию:
(x+7) *(x+1) - (x+6) * x = 15x^2 + x + 7x - x^2 - 6x = 15   
2x=8     
x=4(ширина бас.);       
4+6=10 (длина бас.).

Answer 2

Calculation of the Pool Area

To calculate the area of the pool, we need to determine the dimensions of the pool itself. According to the given information, the pool has a rectangular shape, with one side being 6 meters longer than the other. Additionally, the pool is surrounded by a track that is 0.5 meters wide, and the total area (including the pool and the track) is 15 square meters.

Let's denote the shorter side of the pool as x meters. Therefore, the longer side of the pool would be x + 6 meters.

To calculate the area of the pool, we need to subtract the area of the track from the total area. The area of the track can be calculated by multiplying the width of the track (0.5 meters) by the perimeter of the pool.

The perimeter of the pool can be calculated by adding the lengths of all four sides. Since the pool has a rectangular shape, opposite sides have the same length.

Now, let's calculate the area of the pool step by step:

1. Calculate the perimeter of the pool: - The perimeter is equal to twice the sum of the lengths of the shorter and longer sides of the pool. - Perimeter = 2 * (x + (x + 6)) = 2 * (2x + 6) = 4x + 12 meters.

2. Calculate the area of the track: - The area of the track is equal to the width of the track (0.5 meters) multiplied by the perimeter of the pool. - Area of the track = 0.5 * (4x + 12) square meters.

3. Calculate the area of the pool: - The area of the pool is equal to the total area (15 square meters) minus the area of the track. - Area of the pool = 15 - (0.5 * (4x + 12)) square meters.

Now, let's solve for the value of x and calculate the area of the pool.

Solution:

To find the value of x, we can set up an equation using the given information:

Area of the pool = x * (x + 6) square meters

We can then solve this equation to find the value of x.

Let's calculate the area of the pool:

Area of the pool = 15 - (0.5 * (4x + 12)) square meters

Now, let's solve the equation:

x * (x + 6) = 15 - (0.5 * (4x + 12))

Expanding the equation:

x^2 + 6x = 15 - 2x - 6

Simplifying the equation:

x^2 + 8x - 9 = 0

To solve this quadratic equation, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 1, b = 8, and c = -9.

Calculating the discriminant (b^2 - 4ac):

Discriminant = 8^2 - 4 * 1 * -9 = 64 + 36 = 100

Since the discriminant is positive, we have two real solutions for x.

Using the quadratic formula:

x = (-8 ± √100) / (2 * 1)

Calculating the square root of 100:

√100 = 10

Simplifying the equation:

x = (-8 ± 10) / 2

Calculating the two possible values of x:

x1 = (-8 + 10) / 2 = 2 / 2 = 1

x2 = (-8 - 10) / 2 = -18 / 2 = -9

Since the length of a side cannot be negative, we discard the solution x2 = -9.

Therefore, the value of x is 1 meter.

Now, let's calculate the area of the pool using the value of x:

Area of the pool = 1 * (1 + 6) = 1 * 7 = 7 square meters.

Answer:

The area of the pool is 7 square meters.