Question 838181: the third rectangular prism has the following characteristics:
-it has a volume of 70 cubic inches
-the lengths of the edges are all prime numbers
-the difference between two of the dimensions is 3, and the difference between a different pair of dimensions is 5.
-What are the dimensions of the rectangular prism?
Thank you for your help. My daughter is in 5th grade, and missed the class because she was sick and her teacher is well lets just say not very helpful.
thank you,
kim
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! Volume = length * width * height
and that product has to be 70.
Prime numbers are 2, 3, 5, 7, 11, 13, ...
They are numbers that have only two different factors: 1 and the number itself.
In other words, they are not 1, and are only divisible by 1 and themselves.
6 is not prime because we can write it as
 , and as  .
It has four factors, so it is not prime.
On the other hand, 13 can only be written as
 , so it has just two factors: 1 and 13.
It is not divisible by anything else.
1 is not a prime number
The only set of three prime numbers whose product is 70 is 2, 5, and 7.
Luckily they comply with the other two conditions:
5 - 2 = 3 (the difference between two of the dimensions is 3), and
7 - 2 = 5(the difference between a different pair of dimensions is 5).
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