Answer:
The width of the tank is 5 feet.
Step-by-step explanation:
Given:
A tank's length is 3 feet longer than its width.
The height is 1 foot less than the width.
The volume of the tank is 160 cubic feet.
Now, to find the width of the tank.
Let the width of the tank be [tex]x.[/tex]
So, length is [tex]x+3.[/tex]
And, height is [tex]x-1.[/tex]
The volume of tank = 160 cubic feet.
Now, to get the width we put formula:
Volume = length × width × height.
[tex]160=(x+3)\times x\times (x-1)[/tex]
[tex]160 =x(x^2-x+3x-3)[/tex]
[tex]160=x(x^2+2x-3)[/tex]
[tex]160=x^3+2x^2-3x[/tex]
Subtracting both sides by 160 we get:
[tex]0=x^3+2x^2-3x-160[/tex]
[tex]x^3+2x^2-3x-160=0[/tex]
Now, on solving the equation we get:
[tex]x=5.[/tex]
The width = 5 feet.
Therefore, the width of the tank is 5 feet.
