The dimensions of a cuboid are in the ratio 5:3:1 and its total surface area is `414\ m^2dot` Find the dimensions.

Explanation

We know the formula for total surface area `=2(lb+bh+hl)`
Given
Ratio` = 5:3:1`
`:. l:b:h=5:3:1=5x:3x:x`
So A/Q we can write
`2(lb+bh+hl)= 414m^2`
`2(5x**3x+3x**x+x**5x)=414m^2`
`15x^2+3x^2+5x^2=207`
`23x^2=207`
`x^2=207/23`
`x=sqrt9`
`x=3`
So length (l)= `5*3=15`m
breath(b)= `3*3= 9`m
height (h)=`3*1=3`m