THE CARDBOARD BOX.
(
Patchwork Puzzles)
This puzzle is not difficult, but it will be found entertaining to
discover the simple rule for its solution. I have a rectangular
cardboard box. The top has an area of 120 square inches, the side 96
square inches, and the end 80 square inches. What are the exact
dimensions of the box?
Answer:
The areas of the top and side multiplied together and divided by the
area of the end give the square of the length. Similarly, the product of
top and end divided by side gives the square of the breadth; and the
product of side and end divided by the top gives the square of the
depth. But we only need one of these operations. Let us take the first.
Thus, 120 x 96 divided by 80 equals 144, the square of 12. Therefore the
length is 12 inches, from which we can, of course, at once get the
breadth and depth--10 in. and 8 in. respectively.
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