Difference between revisions of "2019 AMC 8 Problems/Problem 2"

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Solution to AMC 8 Problem 2 2019:
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==Solution 1==
  
 
We know that the length of the shorter side of the 3 identical rectangles are all 5 so we can use that by seeing that the longer side of the right rectangle is the same as 2 of the shorter sides of the other 2 left rectangles. This means that <math>2\cdot{5}\ = 10</math> which is the longer side of the right rectangle, and because all the rectangles are congruent, we see that each of the rectangles have a longer side of 10 and a shorter side of 5. Now the bigger rectangle has a shorter length of 10(because the shorter side of the bigger rectangle is the bigger side of the shorter rectangle, which is 10) and so the bigger side of the bigger rectangle is the bigger side of the smaller rectangle + the smaller side of the smaller rectangle, which is <math>10 + 5 = 15</math> . Thus, the area is <math>15\cdot{10}\ = 150</math>  for choice <math>\boxed{\textbf{(E)}\ 150}</math>                  ~~Saksham27
 
We know that the length of the shorter side of the 3 identical rectangles are all 5 so we can use that by seeing that the longer side of the right rectangle is the same as 2 of the shorter sides of the other 2 left rectangles. This means that <math>2\cdot{5}\ = 10</math> which is the longer side of the right rectangle, and because all the rectangles are congruent, we see that each of the rectangles have a longer side of 10 and a shorter side of 5. Now the bigger rectangle has a shorter length of 10(because the shorter side of the bigger rectangle is the bigger side of the shorter rectangle, which is 10) and so the bigger side of the bigger rectangle is the bigger side of the smaller rectangle + the smaller side of the smaller rectangle, which is <math>10 + 5 = 15</math> . Thus, the area is <math>15\cdot{10}\ = 150</math>  for choice <math>\boxed{\textbf{(E)}\ 150}</math>                  ~~Saksham27
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==See Also==
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{{AMC8 box|year=2019|before=1|num-a=2}}
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{{MAA Notice}}

Revision as of 00:43, 20 November 2019

Solution 1

We know that the length of the shorter side of the 3 identical rectangles are all 5 so we can use that by seeing that the longer side of the right rectangle is the same as 2 of the shorter sides of the other 2 left rectangles. This means that $2\cdot{5}\ = 10$ which is the longer side of the right rectangle, and because all the rectangles are congruent, we see that each of the rectangles have a longer side of 10 and a shorter side of 5. Now the bigger rectangle has a shorter length of 10(because the shorter side of the bigger rectangle is the bigger side of the shorter rectangle, which is 10) and so the bigger side of the bigger rectangle is the bigger side of the smaller rectangle + the smaller side of the smaller rectangle, which is $10 + 5 = 15$ . Thus, the area is $15\cdot{10}\ = 150$ for choice $\boxed{\textbf{(E)}\ 150}$ ~~Saksham27

See Also

2019 AMC 8 (ProblemsAnswer KeyResources)
Preceded by
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Followed by
Problem 2
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