Answer:
Width 2 2/3 cm , length = 9 cm.
Step-by-step explanation:
V = 96 = 1/3 * 12 * x(3x + 1)
x (3x + 1) = 96 / (1/3 * 12)
x(3x + 1) = 24
3x^2 + x - 24 = 0
3x^2 + 9x - 8x - 24 = 0
3x(x + 3) - 8(x + 3) = 0
(3x - 8)(x + 3) = 0
x = 8/3 , -3 ( we ignore the negative root).
x = 8/3 = width , so the length = 3 * 8/3 + 1 = 9 cm.
So the width of the base = 2 2/3 cm and the length = 9 cm.
