Answer:
20 in, 40 in
Step-by-step explanation:
Let L is the length and W is the width.
Total distance around, P = 2 L + 2 W = 120
L + W = 60 ..... (1)
Volume of box, V = W² x L
V = W² x (60 - W) from equation (1)
V = 60 W² - W³
dV/dW = 120 W - 3W²
It is equal to zero for maxima and minima
120 W - 3 W² = 0
W = 40 in
L = 60 - 40 = 20 in
Thus, the dimensions of the box is L = 20 in, W = 40 in
