the volume of a rectangular prism is 144 cubic inches. The height of the prism is 8 inches. Which measurments, in inches, could be the dimensions of the base?

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You divide 144 cubic inches by 8 inches (height) because you must use inverse operations on both sides of the equation to isolate the length x width. The inverse operation of multiplication is division, so the following is the application of division to the problem, broken down:

`144=l times w...

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You divide 144 cubic inches by 8 inches (height) because you must use inverse operations on both sides of the equation to isolate the length x width. The inverse operation of multiplication is division, so the following is the application of division to the problem, broken down:

`144=l times w times 8`

`144 div 8=l times w times 8 div 8`

`18=l times w`

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If the volume V = 144 cubic inches, and V = length*width*height, 

then 144 cubic inches = length*width*8 inches

and length*width = 144/8 square inches = 18 square inches.

 

This means that the length and width can be any pair of numbers that has a product of 18.

Examples: 2*9, 1*18, 1/2*36, etc.

Keep in mind that the dimensions aren't necessarily whole numbers! There are actually infinitely many answers to this problem, so think of a way to describe the solution set in general terms. 

Approved by eNotes Editorial Team