2019 AMC 8 Problems/Problem 2
Problem 2
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 ?
Solution 1
We can see that there are 2 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 5 (Because the problem says so) and the bigger side is 10 (Double 5). Now we get the sides of the big rectangles being 15 and 10 so the area is . ~avamarora
Solution 2
Using the diagram we find that the larger side of the small rectangle is 2 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 . ~~fath2012
Solution 3
We see that if the short sides are 5, the long side has to be because the long side is equal to the 2 short sides and because the rectangles are congruent. If that is to be, then the long side of the BIG rectangle(rectangle ) is because long side + short side of the small rectangle is . The short side of rectangle is because it is the long side of the short rectangle. Multiplying and together gets us which is . ~~mathboy282
(also includes problems 1-10)= https://www.youtube.com/watch?v=5i69xiEF-pk&t=2s