Grades 9-10 Video Solutions 2024-2024_9-10

Video Transcription

Arthur encloses a rectangular field with 40 meters of fence. The side lengths of the field are all prime numbers. What is the maximum possible area of the field?  Because the perimeter of the fence is 40, we know that the length and width must add up to 20.  We also know that the length and width must be prime numbers. Then we can just go through all  the possible prime numbers pairs of prime numbers that sum to 20 and we find that only 3 and 17  as well as 7 and 13 sum up to 20. Checking the products of these we find that 3 times 17 is 51 and 7 times 13 is 91 and therefore the maximum possible area of the field is 91.

Video Summary

Arthur encloses a rectangular field with 40 meters of fence. The side lengths of the field are all prime numbers. What is the maximum possible area of the field? Because the perimeter of the fence is 40, we know that the length and width must add up to 20. We also know that the length and width must be prime numbers. Then we can just go through all the possible prime numbers pairs of prime numbers that sum to 20 and we find that only 3 and 17 as well as 7 and 13 sum up to 20. Checking the products of these we find that 3 times 17 is 51 and 7 times 13 is 91 and therefore the maximum possible area of the field is 91.

Keywords

rectangular field

prime numbers

maximum area

perimeter 40

fence