Two marbles of sizes π and 4π are enclosed in a rectangular box. What is the total area of the box?
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Solution
The rectangle area is 24.
![](https://mirangu.com/wp-content/uploads/2020/11/MarbleBoxSolution.jpg)
The first step is to extend the segment EC. The resulting right triangle AHC is similar to DCE. From the fact that the smaller circle has radius 1 and the bigger radius 2, it follows that their bases have proportion 2. Hence BE is ED and thus BHE and DCE are congruent.
Now it is a matter of filling in the lengths as shown and applying the Pythagorean theorem to arrive at x=4. Hence the original rectangle has size 4 x 6.