Respuesta :
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 = [tex]Length \times Width \times height[/tex]
Volume of solid = [tex](x+1) \times x \times (2x+1)[/tex]
Volume of solid =[tex](x^2+x)(2x+1)[/tex]
Volume of solid =[tex]2x^3+x^2+2x^2+x=2x^3+3x^2+x[/tex]
We are given that a rectangular solid must have a volume of 84 cubic meters
So, [tex]2x^3+3x^2+x=84\\2x^3+3x^2+x-84=0\\(x-3)(2x^2+9x-28)=0\\[/tex]
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.
The volume of a rectangular solid shipping container = 84 cubic meters
The width of the container = 3m
The length of the container = (x + 1) = (3+1) = 4m
The height of the container = (2x + 1) = (2 x 3 + 1) = 7m
Given:
The volume of a rectangular solid shipping container = 84 cubic meters
Let: The width of the container be x
The length of the container must be one meter longer than the width.
So, The length of the container be (x + 1)
The height must be one meter greater than twice the width.
So, The height of the container be (2x + 1)
To find the dimensions of the container
The Volume of the container = Length x Width x Height
[tex]84=x(x+1)(2x+1)[/tex]
[tex]84=(x^{2} +x)(2x+1)[/tex]
[tex]84=2x^{3} +3x^{2} +x[/tex]
[tex]2x^{3} +3x^{2} +x-84=0\\(x-3)(2x^{2} +9x+28)=0\\x-3=0\\x=3[/tex]
So, The width of the container = 3m
The length of the container = (x + 1) = (3+1) = 4m
The height of the container = (2x + 1) = (2 x 3 + 1) = 7m
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