Question

The perimeter of a rectangle is 200 feet. Describe the possible lengths of a side if the area of the rectangle is not to exceed 900 square feet.

The length in feet of a side is in the interval ______ or in the interval ______

Answer 1

Use those values to test your rectangle
When x = 90 y must be less than 10
when x = 10, y must be less than 90

Answer 2

so in interval notation would that be (-inf,10) and (-inf,90) ?

Answer 3

or since it's x and y would it be (90,10) and (10,90)

Answer 4

Let me think about this, we know that the sum of length + width must equal 100 (as perimeter is 200 ft), and the area (length times width) must be less than 900 sq ft.
First there is no negative values as these are dimensions and will be positive. one side will have to fall in this domain larger than zero and less than 10. Letting x be one side then: 0 <x <10. this will of course establish the other side of the rectangle and it will have the domain of (calling the other side y) 100>y>90
Does this help?