Question

Bob wants to fence in a rectangular garden in his yard. He has 86 feet of fencing to work with and wants to use it all. If the garden is to be × feet wide, express the area of the garden as a function of x.

Answer 1

Area = 21.5^2 = 462.25 square feet

Explanation:

If the garden is x feet wide, then it must also be x feet long since it is rectangular. Therefore, the perimeter of the garden is 2x + 2x = 4x. We know that Bob has 86 feet of fencing, so we can set up the equation 4x = 86 and solve for x:

4x = 86

x = 21.5

Therefore, the width of the garden is 21.5 feet and the length is also 21.5 feet.

To find the area of the garden, we multiply the width by the length:

Area = x * x = x^2

Area = 21.5^2 = 462.25 square feet

Answer 2

Let's call the width of the rectangular garden "x" and its length "y". We know that the perimeter of the garden is 86 feet, so we can write an equation:

2x + 2y = 86

Simplifying this equation, we can isolate y:

2y = 86 - 2x

y = 43 - x

The area of the garden is given by the formula:

A = xy

Substituting y with 43 - x, we get:

A = x(43 - x)

Expanding this expression, we get:

A = 43x - x^2

So the area of the garden is a function of x, expressed as A = 43x - x^2