Question

A rectangular piece of metal is 30 in longer than it is wide. Squares with sides 6in long are cut from the four corners and the flaps are folded upward to form an open box. If the volume of the box. Is 3354 in^3, what were the original dimensions of the piece of metal? What is the original width?

Answer 1

check the picture below.


`\bf V=3354~in^3\qquad \qquad 3354=6(w-12)(w+18) \\\\\\ \cfrac{3354}{6}=w^2+6w-216\implies 559=w^2+6w-216 \\\\\\ 0=w^2+6w-775\implies 0=(w+31)(w-25)\implies w= \begin{cases} -31\\ \boxed{25} \end{cases}`


since the width is just a dimension unit, it can't be -31.

what is the length? well, the length is w + 30.