2019 AMC 8
Complete problem set with solutions and individual problem pages
Three identical rectangles are put together to form rectangle , as shown in the figure below. Given that the length of the shorter side of each of the smaller rectangles is 5 feet, what is the area in square feet of rectangle ?
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Solution 1
We can see that there are rectangles lying on top of the other and that is the same as the length of one rectangle. Now we know that the shorter side is , so the bigger side is , if we do . Now we get the sides of the big rectangle being and , so the area is .
Solution 2
Using the diagram we find that the larger side of the small rectangle is times the length of the smaller side. Therefore, the longer side is . So the area of the identical rectangles is . We have 3 identical rectangles that form the large rectangle. Therefore the area of the large rectangle is .
