We are given a rectangle with width $x+2$ and height $x-5$. The area of the rectangle is 800 square meters. We need to find the length of the width and height. The area of a rectangle is given by $A = bh$, where $b$ is the width and $h$ is the height.

1. Problem Description

We are given a rectangle with width $x+2$ and height $x-5$. The area of the rectangle is 800 square meters. We need to find the length of the width and height. The area of a rectangle is given by $A = bh$, where $b$ is the width and $h$ is the height.

2. Solution Steps

We have the equation:

$(x+2)(x-5) = 800$

Expanding the left side, we get:

$x^2 - 5x + 2x - 10 = 800$

$x^2 - 3x - 10 = 800$

$x^2 - 3x - 810 = 0$

We need to solve this quadratic equation for $x$. We can use the quadratic formula or try to factor it. Let's try factoring:

We are looking for two numbers that multiply to -810 and add up to -

3. The numbers are -30 and

2

7. So we can factor the equation as:

$(x - 30)(x + 27) = 0$

Therefore, $x = 30$ or $x = -27$.

Since the width and height must be positive, we choose $x = 30$.

Width = $x + 2 = 30 + 2 = 32$ meters

Height = $x - 5 = 30 - 5 = 25$ meters

3. Final Answer

The width is 32 meters and the height is 25 meters. So the answer is (d).

Final Answer: Ancho= 32 m, altura= 25 m