Question

Un agricultor tiene un terreno cuadrado dedicado al cultivo de hortalizas. Para ampliarlo, quiere comprar el terreno adyacente, que mide de largo lo que mide el lado de su terreno actúa, y de ancho 10 metros. De esa manera, con los dos terrenos juntos, dispondría de 600 metros cuadrados cuanto mide el lado del terreno

Answer 1

Answer: 20 meters.

Step-by-step explanation:

The formula for calculate the area of a square is:

$A=s^2$

Where "s" is the side length of the square:

The formula for calculate the area of a rectangle is:

$A=lw$

Where "l" is the lenght and "w" is the width.

Based on the information provided, you know the sum of the areas of the square land and the adjacent land is 600 m². This is:

$A_1+A_2=600\\\\s^2+lw=600$

Knowing that the width of the adjacent land is 10 meters:

$s^2+10l=600$

Since  the lenght of the adjacent land and the side lenght of his actual land are equal:

$l=s$

You can substitute this into $s^2+10l=600$:

$s^2+10s=600\\\\s^2+10s-600=0$

Applying the Quadratic formula, you get:

$s=\frac{-b\±\sqrt{b^2-4ac} }{2a}\\\\s=\frac{-10\±\sqrt{(10)^2-4(1)(-600)} }{2(1)}\\\\s_1=20\\\\s_2=-30$

Since the side lenght cannot be negative, you can determine that this is:

$s=20\ m$