consider the collection of all rectangles that have lengths 2in. less than twice their widths. find the possible widths(in inches) of these rectangles if their perimeters are less than 200 in

Answer 1

let width be x
so length y = 2x-2

p = 2(x+y) = 2x+2(2x-2) = 6x-4

we want p < 200

6x-4 < 200
6x < 204
x < 34

so, as long as the width is less than 34, the length will be less than 66, and the perimeter will be less than 200.