Problem number 15. A floor is covered with identical rectangular tiles as shown. The shorter side of each tile is one meter. What is the length of the side with the question mark? A, 6 meters. B, 8 meters. C, 10 meters. D, 11 meters. E, 12 meters. The problem and the picture show us that the shorter side of each rectangle is one meter. M stands for meter here. Looking at the picture, we can find the length of the longer side of each rectangle. Then we can figure out the total length. We can find several places in this picture where the longer side of the smaller rectangle, like this one, is lined up to some shorter sides of the rectangle. For example, we have this here. And we see that the length of the longer side of the rectangle is the same as 1, 2, 3, 4 shorter sides. Remember, all these rectangles are identical. That means that if this is 4 meters, because 1 meter times 4 is 4 meters, then each one of these sides will be 4 meters as well. Now we can use this information to find the length along the bottom here. We know that each short side is one meter, so that's one meter up here. Each of these is going to be one meter. Each of these is going to be one meter. And this is one meter. The longer side is 4 meters. So we have 1 meter plus 4 meters plus 1 meter plus 1 meter plus 4 meters plus 1 meter, which is 4 plus 4 is 8 meters, plus 1, 2, 3, 4. 4 lengths of 1 meter, or 4 meters, which gives us a total of 12 meters. So our answer is E, 12 meters.

rectangular tiles

tile arrangement

side length calculation

geometry problem

12 meters