Let
x--------> the length side of the square base of the box
y-------> the height of the box
V------> volume of the box
we know that
V=x²*y
V=150 in³
so
150=x²*y------> equation 1
y=1.5*x------> equation 2
substitute the equation 2 in equation 1
150=x²*[1.5*x]-----> x³=150/1.5------> x³=100
x=4.64 in
y=1.5*4.64-----> y=6.96 in
therefore
the answer is
the length side of the square base of the box is 4.64 in
the height of the box is 6.96 in
