Find the length, width and height of the box

[jasen]

I know this math problem is easy for the master here, But it will be interesting for new members

 

I have a box,
rasio of the three surface area are 1:5:10
If the volume of the box is 160m^3
find the length, width and height of the box

 

[tojo928]

Spoiler

2X4X20

Areas 8:40:80

since 160 broken down into its base is 5x2⁵. this meant that since the ratios of B and C both contained a factor of 5, the shared side had to be a multiple of 5*2^x. the rest had to be 2^x where the sum of the 3 unknown powers had to sum to 5. This takes you to a very limited number of possibilities which are easy enough to just calculate.