Question

the volume of a storage tub shaped like a rectangular prism is 24 ft cubed. The height of the top is 3 ft the width is W feet in the length is W + to use the formula V equals l w h to find the value of w

Answer 1

`\boxed{W=2ft}`

Explanation:

A prism is a solid object having two identical bases, hence the same cross section along the length. Prism are called after the name of their base. On the other hand, a rectangular prism is a solid whose base is a rectangle. Multiplying the three dimensions of a rectangular prism: length, width and height, gives us the volume of a prism:

`V=L* W* H`

From the statement of the problem we know:

`V=24ft^3 \\ \\ H=3ft \\ \\ W=W \\ \\ L=W+2`

So:

`24=(W+2)(W)(3) \\ \\ 3W(W+2)=24 \\ \\ 3W^2+6W-24=0 \\ \\ From \ the \ Quadratic \ Formula: \\ \\ W_(12)=(-b \pm √(b^2-4ac))/(2a) \\ \\ W_(12)=(-6 \pm √(6^2-4(3)(-24)))/(2(3)) \\ \\ W_(1)=2 \\ \\ W_(2)=-4`

Since we can't have negative distance, the only valid option is
`\boxed{W=2ft}`