Question

a right rectangular prism has a volume of 144 cubic centimeters and a height of 4 centimeters water a possible length and width in centimeters of the prism

Answer 1

Volume of rectangular prism = length x width x height

Height = 4 cm

volume(v) = 144 cubic centimeter

`\begin{gathered} V\text{ =Length x width x 4} \\ 144=\text{ length x width x 4} \\ (144)/(4)=\frac{length\text{ x width x 4}}{4} \\ 36\text{ = length x width} \end{gathered}`

The possible length and width could be factors of 36

These include 9cm and 4cm, 2cm and 18cm , 12cm and 3cm

So possible values for the length = 9cm or 18cm or 12cm

possible values for the width = 4cm or 2cm or 3cm

So factors of 36 = 2 x2 x 3 x3

We combine these factors to give us just two unequal factors since it is a rectangle and not a square

so these factors are

4x9

2x18

and

3 x 12

By assumption though, the length is always longer than the width, hence I assigned the longer/larger values to the length and the shorter/smaller values to the width. Hence the answers above.