A box with no top is to be constructed from a piece of cardboard whose width measures $x \mathrm{~cm}$ and whose length measures $3 \mathrm{~cm}$ more than its width. The box is to be formed by cutting squares that measure $1 \mathrm{~cm}$ on each side from the four corners, and then folding up the sides. If the volume of the box will be $130 \mathrm{~cm}^{3}$, what are the dimensions of the piece of cardboard?
A) $15 \mathrm{~cm}$ by $12 \mathrm{~cm}$
B) $23 \mathrm{~cm}$ by $16 \mathrm{~cm}$
C) $18 \mathrm{~cm}$ by $15 \mathrm{~cm}$
D) $19 \mathrm{~cm}$ by $16 \mathrm{~cm}$

Question

Quizplus · Accepted Answer

The length of the cardboard is $x+3$ cm. The width of the cardboard is $x$ cm. The height of the box is $1$ cm. The volume of the box is $130 \mathrm{~cm}^{3}$. So, we have:$$(x+3)x(1)=130$$$$x^2+3x-130=0$$$$(x+13)(x-10)=0$$$$x=-13,10$$Since $x$ is a length, it must be positive. So, $x=10$. The length of the cardboard is $10+3=13$ cm. The width of the cardboard is $10$ cm. So, the dimensions of the piece of cardboard are $13 \mathrm{~cm}$ by $10 \mathrm{~cm}$.

A Box with No Top Is to Be Constructed from a Piece