Question

A farmer creates a rectangular pen using part of the wall of a barn for one side of the pen and a total of 130 feet of fencing for the remaining 3 sides, as shown in the diagram. Write an equation which gives the area of the pen, A, as a function of x, the length of fence parallel to the barn wall.

Answer 1

A = (130x - 2x^2)/2

Explanation:

Let's break down the information given in the problem:

• The rectangular pen has one side formed by the wall of the barn.
• The other three sides of the pen are made of fencing.
• The total length of the fencing used for the three sides is 130 feet.

To write an equation that gives the area of the pen, A, as a function of x, the length of fence parallel to the barn wall, we need to consider the dimensions of the pen.

Let's assume the length of the pen parallel to the barn wall is x. In that case, the width of the pen (the side perpendicular to the barn wall) would be (130 - 2x)/2, considering that there are two equal sides of length x and the remaining fencing is used for the width.

The area of a rectangle can be calculated by multiplying its length and width. Therefore, the equation that gives the area of the pen, A, as a function of x is:

A = x * (130 - 2x)/2

Simplifying this equation further, we have:

A = (130x - 2x^2)/2

So, the equation is A = (130x - 2x^2)/2, where A represents the area of the pen and x represents the length of the fence parallel to the barn wall.