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

Answer:

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

Step-by-step 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

$Length = \frac{42x^3 - 14x^2 + 21x}{7x}$

Factorize the numerator

$Length = \frac{7x(6x^2 - 2x + 3)}{7x}$

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