Rachel had a box in the shape of a prism with a square base. the capacity of the box is 150 cubic inches. the height of the box (y) is 1 1/2 times the base of the box (x). find the approximate height and the length of the box

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

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