An open box with a rectangular base of x inches by x+4 inches has a height of 6 inches. The volume of the box is 702 cubic inches. Find the dimensions of the box.
A) 11 inches by 15 inches by 6 inches
B) 9 inches by 13 inches by 6 inches
C) 15 inches by 19 inches by 6 inches
D) 13 inches by $17$ inches by 6 inches
E) $13$ inches by $15$ inches by 6 inches

Question

Quizplus · Accepted Answer

The volume of the box is given by $V=x(x+4)6=6x^2+24x=6(x^2+4x)$. Setting this equal to 702 and factoring, we have \begin{align*}
6(x^2+4x)&=702\
x^2+4x&=117\
x^2+4x-117&=0\
(x+13)(x-9)&=0
\end{align*} Since $x$ must be positive, we have $x=9$. Plugging this in, we get the dimensions of the box to be $9$ inches by $13$ inches by $6$ inches. Therefore, the answer is B.

An Open Box with a Rectangular Base of X Inches 171717

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