Good morning! Recall that perimeter of a rectangle is the sum of the lengths of all sides, so:
P= L + L + W + W, or P + 2L + 2W
If the width is 31 and total perimeter is at least 692, then the minimum would be:
692 = 2L + 2(31), or 692 = 2L + 62
Subtract 62 from both sides:
630 = 2L
Divide both sides by 2:
315 = L
Remember that the perimeter is at least 692; therefore the length would be at least 315 cm
Hope this helps
Mike
12/16/2013

Michael W.