A 5cm by 5cm square is cut from each corner of a rectangular piece of cardboard. The sides are folded up to make an open box with a maximum volume.If the perimeter of the base is 50 cm. what are the dimension of the box?
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Answer:
12.5cm long, 12.5cm wide, 5 cm high
Step-by-step explanation:
2x + 2y = 50
x + y = 25
y = 25-x
V = 5xy
= 5x(25-x)
V= 125x -
dV/dx = 125 - 10x = 0 for a max of V
10x/10 = 125 /10
x = 12.5
y = 25-12.5 -> y=12.5