Question

Write an inequality representing the fact that the total perimeter of the garden is at most 40 ft

Answer 1

Part A)
`x+y\leq 20`

Part B) The solution in the attached figure

Explanation:

The complete question is

Suppose Rick has 40 ft of fencing with which he can build a rectangular garden. Let X represent the length of the garden and let Y represent the width.

A. Please write an inequality representing the fact that the total perimeter of the garden is at most 40 ft.

B. Please sketch part of the solution set for this inequality that represents all possible values for the length and width of the garden.

Part A)

Let

x ----> the length of the rectangular garden

y ----> the width of the rectangular garden

we know that

The perimeter of the rectangular garden is equal to

`P=2x+2y`

In this problem the word "at most" means "less than or equal to"

so

The inequality that represent this situation is

`2x+2y\leq 40`

Simplify

`x+y\leq 20`

Part B) we have

`x+y\leq 20`

Isolate the variable y

subtract x both sides

`y\leq -x+20`

The solution of the inequality is the shaded area below the solid line
`y= -x+20`

The slope of the solid line is negative (m=-1)

The y-intercept of the solid line is (0,20)

The x-intercept of the solid line is (20,0)

therefore

The solution is the triangular shaded area

see the attached figure

Remember that

Both the length and the width must be positive