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in quadrilateral abcd each of the side lengths is an integer, and ad=bc. have ab:ad=2:5 and ad:cd=3:4, then what is the smallest possible perimeter of the quadrilateral?

 Aug 25, 2021
 #1
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Hi guest! I have thought about this question for a bit and since it's says in the first ratio that ad=5 but then it says in the second one that ad=3 it has to be something divisible by 3 AND 5, it says to find the smallest perimeter so ad has to be the lcm of 3 and 5 which is 15, in the first ratio 15 is divided by 3 to get 5 therefore ab has also been divided by 3 so ab=6, applying the same logic to the other ratios 15 was divided by 5 to get 3 therefore cd was also divided 5. If ad=ab then we get

ab=6

bc=15

cd=20

ad=15

Add these together to get 56.

Could someone check this? Idk if I have explained it well

 

 

 

 

SCZ

 Aug 25, 2021
 #2
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AB = 2*4 = 8 laugh

Guest Aug 25, 2021

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