SOLUTION: a box with height (x+5) cm has a square base with side x cm. a secong box with height (x+2) cm has a aquare base with side (x+1) cm. if the two boxes have the same volume, find the

Question 231604: a box with height (x+5) cm has a square base with side x cm. a secong box with height (x+2) cm has a aquare base with side (x+1) cm. if the two boxes have the same volume, find the x value
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

The volume of a rectangular solid is given by:

So for your first box:

And for the second box:

(verification left as an exercise for the student.)

Set these two volumes equal to each other:

Collect like terms:

Leaving a quadratic that unfortunately does not factor. Use the quadratic formula:

Of the two roots, one will be negative -- finding them is left as an arithmetic exercise for the student. Discard the negative root because you are looking for a positive measure of length. Hint: Leave your answer in radical form for the exact answer -- at least until you have verified that the root you obtained is the correct answer by using it to calculate the volume of each of the boxes and making sure they are equal quantities -- another exercise for the student.

John

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