Answer:
Step-by-step explanation:
As the base is a square so the length is a, width is a and the height is h.
According to the question,
a + a + h = 96
h = 96 - 2a .... (1)
Volume of the box, V = length x width x height
V = a x a x h
V = a² (96 - 2a) from equation (1)
V = 96a² - 2a³
Differentiate both sides
[tex]\frac{dV}{da}=192 a -6a^{2}[/tex]
Now put it equal to zero.
192 a - 6a² = 0
a = 32 in
h = 96 - 2 x 32
h = 32 in
Thus, the length and the width os teh base is 32 in and the height is 32 in.
