Question

An art student is searching for a rectangular canvas to paint on. His professor requires that the height and width of each canvas exceed 12 inches, but because of the lack of framing materials, the perimeter cannot exceed 60 inches. Which of the following systems correctly describe the possible lengths (l) and width (w) of the canvas?

Answer 1

60(is less than or eual to) (2l)+(2w)
l>12
w>12

plug in the values
60(is less than or equal to) (2*15)+(2*15)
the above solution is only one. values for l and w must be greater than 12 but less than or equal to 15

Answer 2

Answer: The canvas is a rectangle, so the perimeter of the canvas is P = 2*H + 2*W, where H is the height and W is the width.

the problem says that P < 60 inches, also H and W must be > 12 inches.

now, 2*H + 2*W < 60 inches.

H + W < 30 inches.

H < 30 inches - W.

the minimum value of W is 12 inches, this means that the maximum value of H is: H <30 inches - 12 inches = 18 inches.

So if W = 12 inches, then H must have less than 18 inches.

if W = 13 inches, then H must have less than 17 inches.

if W = 14, then H<16

if W = 15, then H <15.. and so on.

The set is described as : {H, W; H,W>12 inches / H < 30 inches - W}