rectangles with perimeters

[wrb]

Can you help me find the smallest and largest possible area for rectangles with perimeters of 24 units and whole numbers side lengths. Will you explain how you know your answer is correct.

 

[arthur ohlsten]

2L+2W=24
L+W=12
area=LW
area=L[12-L]
area=12L-L^2

this will help you visualize the problem, plot on rectangular coordinates, W along the y axis and L along the x axis, with L from 0 to 12. The curve rises as L increases and then returns to 0 as L goes to 12

d[area]/dL=12-2L set d[area]/dL=0
0=12-2L
L=6 answer

Arthur
0=L dW/dL+W