Question

The perimeter of a rectangular park must be no greater than 140 meters, because that is the total length of the materials available for the border. The width of the park cannot exceed 24 meters. What are the possible lengths of the park?

Answer 1

Explanation:

the perimeter of a rectangle is

2×length + 2×width

so our inequalities are

2×length + 2×width <= 140 m

length + width <= 70 m

width <= 24 m

let's assume for a moment that width = 24.

and we get

length + 24 <= 70

length <= 46 m

or general

length <= 70 - width

with maximum width (24 m), length <= 46m

with a minimum width (e.g. 1 m), length <= 69

so, overall, 0 m < length < 70 m (I assume width = 0 or length = 0 are not valid).