The main diagonal of a rectangular prism is 31 units n length and each dimension of the rectangular prism is an integer. Find the maximum and minimum possible volume of the rectangular prism.
3 answers
The only dimensions I can think of right off are 5,6,30
Using the following dinky 1980's style program in GW-BASIC
10 for a = 1 to 30
20 for b = 1 to 30
30 for c = 1 to 30
40 if sqr(a*a+b*b+c*c) = 31 then print a,b,c
50 next c
60 next b
70 next a
if got the following:
5,6,30 <------ Steve's answer
6,14,27
6,21,22
14,18,21
My little program actually gave me 24 answers, including all the permutations of the above four.
So now just multiply them to get the volume, and see which is smallest, and which is largest.
10 for a = 1 to 30
20 for b = 1 to 30
30 for c = 1 to 30
40 if sqr(a*a+b*b+c*c) = 31 then print a,b,c
50 next c
60 next b
70 next a
if got the following:
5,6,30 <------ Steve's answer
6,14,27
6,21,22
14,18,21
My little program actually gave me 24 answers, including all the permutations of the above four.
So now just multiply them to get the volume, and see which is smallest, and which is largest.
nicely done. Good luck finding those by hand.
1 answer