Sanchez has a garage on his property. He recently purchased a tractor and cannot fit in his garage. To store is new purcahse, he deices to attach a three-sided fence to one of the walls of his garage in order to save material. If Sanchez has 60 meters of fencing and wants a 400 m^2 area, what will the dimensions of the rectangular fenced area?

To determine the dimensions of the rectangular fenced area, we need to consider the given information.

Let's assume the width of the rectangular fenced area is x meters. Since there are three sides to be fenced, two sides will have the length x, and the side attached to the garage will have the length L.

The perimeter of the fenced area is the sum of the lengths of all three sides. In this case, it is the sum of x + x + L, which is equal to 60 meters.

So, we have the equation: 2x + L = 60.

Now, we need to find the area of the rectangular fenced area. The area of a rectangle is given by the product of its length and width. In this case, it is x * L, which is equal to 400 square meters.

So, we have the equation: x * L = 400.

To find the dimensions, we need to solve these two equations simultaneously.

From the first equation, we can express L in terms of x: L = 60 - 2x.

Substituting this value of L into the second equation, we get: x * (60 - 2x) = 400.

Simplifying this equation, we have: 60x - 2x^2 = 400.

Rearranging it further, we get the quadratic equation: 2x^2 - 60x + 400 = 0.

Now, we can solve this quadratic equation using factoring, completing the square, or the quadratic formula.

After solving the quadratic equation, we find that x has two possible values: x = 10 or x = 20.

Substituting these values of x back into the equation L = 60 - 2x, we find that when x = 10, L = 40 and when x = 20, L = 20.

Therefore, the dimensions of the rectangular fenced area could be either 10 meters (width) by 40 meters (length) or 20 meters (width) by 20 meters (length).

each of the two equal sides ---- x

the single side ------- y

given: 2x + y = 60
y = 60-2x

area = xy = x(60-2x)

x(60-2x) = 400

expand, and solve the quadratic