Question

The height of a rectangular box is 4ft. The length is 2 ft longer than thrice the width x . The volume is 480^3
what's the length and the width

Answer 1

SOLUTION

From the question

$\begin{gathered} \text{height of the box h = 4ft} \\ \text{width = x} \\ \text{length = 2 + 3x} \\ \text{Volume = 224ft}^3 \end{gathered}$

Since the length is 2ft longer than trice the width, the length = 2 + 3x, since the width is given as x.

Now, the box is a cuboid. volume of a cuboid is given as

$V=length\times width\times height$

So the equation becomes

$\begin{gathered} V=l\times x\times h \\ 224=(2+3x)\times x\times4 \\ 224=(2+3x)4x \\ 224=8x+12x^2 \\ \\ 12x^2+8x-224=0 \end{gathered}$