Question

Jeffrey has an aquarium in the shape of a rectangular prism. He is going to place a layer of sand over the base for his iguana. The area of the base of the aquarium can be represented by the expression (42x3−14x2+21x) feet3. If the width of the aquarium is represented by the expression (7x) feet, what is the length of the aquarium?

Answer 1

`Length = 6x^2 - 2x + 3`

Explanation:

Given

`Area = 42x^3 - 14x^2 + 21x`

`Width = 7x`

Required

Determine the length of the aquarium

The area of a rectangular base is calculated as:

`Area = Length * Width`

Substitute values for Area and Width

`42x^3 - 14x^2 + 21x = Length * 7x`

Make Length the subject

`Length = (42x^3 - 14x^2 + 21x)/(7x)`

Factorize the numerator

`Length = (7x(6x^2 - 2x + 3))/(7x)`

`Length = 6x^2 - 2x + 3`