Question 16. Bob makes a square from 4 rectangular pieces. 3 of the pieces are shown. Which of the following is the 4th piece he uses? Let's start off by looking at the pieces that we know of. The first piece is made up of 8 blocks. The next piece, 10 blocks. And the last piece, 6 blocks. Let's get the sum total of how many blocks we use for these. 24. Now, let's find the total number of blocks that are used in the solution pieces. We'll have 15 in A, 5 in B, 6 in C, 12 in D, and 12 in E. Now, we know that we will end up with a square. One of the most important things that makes a square a square is that its height and width are the same. So, let's make some theoretical squares. A square could be 5x5, 6x6, or 7x7. If a square was 5x5 blocks, then it would have a total of 25 blocks. If it was 6x6, it would have 36. And if it was 7x7, it would have 49. We can immediately cross off 49, because none of the other solutions gives us a sum when added to 24. Similarly, we can cross off 25. First of all, we have a piece that is 1x6 blocks, so that cannot even be the solution. Secondly, we are already using 24 blocks. We could only add one more, and that is not a potential solution. So, let's try to make a square that is 6x6 blocks. We can cross out A, B, and C, since we know that we have 24 blocks, and we need 12 more, so either D or E. We will take our first piece, the 1x6 piece, lay it as such. Then we will take the one that is 5 tall, and lay it as such, building a framework that is 6x6, taking our third piece like so. And then to fill in the square, we will add these blocks. Now we take a look at our two answers, D and E. And if we take the blue blocks that we have added, and turn them 90 degrees, we will see that our answer will be E.

square completion

rectangular pieces

6x6 square

block puzzle

solution option E