Question

Un jardín rectangular de 50 m de largo por 34 m de ancho está rodeado por un camino de arena uniforme.Halla la anchura de dicho camino si se sabe que su área es 540 metros

Answer 1

To find the width of the path, we can set up an equation using the area of the path and solve for x. By rearranging the equation and using the quadratic formula, we can find two possible values for x. The positive solution gives us the width of the path, which is around 5.626 meters.

Step-by-step explanation:

In this problem, we have a rectangular garden with dimensions 50 m by 34 m. The garden is surrounded by a uniform-width path. Let's assume the width of the path is 'x' meters.

Since the path is surrounding the garden on all four sides, we need to subtract the length and width of the garden from the length and width of the whole rectangular area. The equation for the area of the path is (50 + 2x)(34 + 2x) - 50 * 34 = 540. Now, we can solve this equation to find the width of the path.

Expanding and simplifying the equation, we get:

1084x + 4x^2 = 540

Rearranging the equation, we have:

4x^2 + 1084x - 540 = 0

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

x = (-b ± sqrt(b^2 - 4ac))/(2a)

Substituting the values of a, b, and c into the formula, we get:

x = (-1084 ± sqrt(1084^2 - 4 * 4 * -540))/(2 * 4)

Calculating x using a calculator, we find two possible values for x: x ≈ -0.126 or x ≈ 5.626. Since the width can't be negative, we disregard the negative solution. Therefore, the width of the path is approximately 5.626 meters.

Answer 2

`h = 3.214\,m`

Step-by-step explanation:

El área total del camino es el producto del perímetro del jardín y el ancho del camino:

`A = 2\cdot (w + l) \cdot h`

Donde:

`w` - El ancho del jardín, en metros.

`l` - El largo del jardín, en metros.

`h` - El ancho del camino, en metros.

El ancho del camino es:

`h = (A)/(2\cdot (w+l))`

`h = (540\,m^(2))/(2\cdot (50\,m + 34\,m))`

`h = 3.214\,m`