Answer:
The Length , width and height of solid are 4 feet , 3 feet and 7 feet respectively.
Step-by-step explanation:
Let the width of rectangular solid be x
We are given that the length of the container must be one meter longer than the width
So, Length of solid = x+1
We are also given that height must be one meter greater than twice the width
So, Height of solid = 2x+1
So, Volume of solid = ![Length \times Width \times height](https://tex.z-dn.net/?f=Length%20%5Ctimes%20Width%20%5Ctimes%20height)
Volume of solid = ![(x+1) \times x \times (2x+1)](https://tex.z-dn.net/?f=%28x%2B1%29%20%5Ctimes%20x%20%5Ctimes%20%282x%2B1%29)
Volume of solid =![(x^2+x)(2x+1)](https://tex.z-dn.net/?f=%28x%5E2%2Bx%29%282x%2B1%29)
Volume of solid =![2x^3+x^2+2x^2+x=2x^3+3x^2+x](https://tex.z-dn.net/?f=2x%5E3%2Bx%5E2%2B2x%5E2%2Bx%3D2x%5E3%2B3x%5E2%2Bx)
We are given that a rectangular solid must have a volume of 84 cubic meters
So, ![2x^3+3x^2+x=84\\2x^3+3x^2+x-84=0\\(x-3)(2x^2+9x-28)=0\\](https://tex.z-dn.net/?f=2x%5E3%2B3x%5E2%2Bx%3D84%5C%5C2x%5E3%2B3x%5E2%2Bx-84%3D0%5C%5C%28x-3%29%282x%5E2%2B9x-28%29%3D0%5C%5C)
On equating
x-3=0
x=3
So, Length of solid = x+1=3+1 = 4 feet
Height of solid = 2x+1 =2(3)+1=7 feet
Width of solid = 3 feet
Hence The Length , width and height of solid are 4 feet , 3 feet and 7 feet respectively.