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

Answer:

$\boxed{W=2ft}$

Step-by-step 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:

$V=L\times W\times H$

From the statement of the problem we know:

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

So:

$24=(W+2)(W)(3) \\ \\ 3W(W+2)=24 \\ \\ 3W^2+6W-24=0 \\ \\ From \ the \ Quadratic \ Formula: \\ \\ W_{12}=\frac{-b \pm \sqrt{b^2-4ac}}{2a} \\ \\ W_{12}=\frac{-6 \pm \sqrt{6^2-4(3)(-24)}}{2(3)} \\ \\ W_{1}=2 \\ \\ W_{2}=-4$

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