How to draw a grid of area of 12 square centimeters and a perimeter of 16 centimeters?

Alright, so if w is the width and l is the length, we have 2w+2l=16 (for the perimeter) and w*l=12. For 2w+2l=16, we can subtract 2l from both sides to get 2w=16-2l, and then divide both sides by 2 to get w=8-l. Substituting that into w*l=12, we get (8-l) * l=12 and - l^2+8l=12. Subtracting 12 from both sides, we get - l^2+8l-12=0. Using the quadratic formula, we get

l = (-8+-sqrt (64 - (4*-1*12)) / - 2 = (-8+-sqrt (16)) / - 2 = (-8+-4) / 2=either 2 or 6. Plugging them into 8-l=w, we get that w is either 2 or 6 too, meaning that you just have to draw the grid with one side being the length of 2 and the other with the length of 6