Solve the problem.
-A piece of cardboard is twice as long as it is wide. It is to be made into a box with an open top by cutting $4 \mathrm {~cm}$ squares from each corner and folding up the sides. Let $x$ represent the width of the original piece of cardboard. Find the width of the original piece of cardboard, $x$, if the volume of the box is $1120 \mathrm {~cm} ^ { 3 }$.
A) $18 \mathrm {~cm}$
B) $17 \mathrm {~cm}$
C) $19 \mathrm {~cm}$
D) $10 \mathrm {~cm}$

Question

Quizplus · Accepted Answer

The original width of the cardboard is $x$ cm, and its length is $2x$ cm. After cutting out $4 \mathrm{~cm}$ squares from each corner and folding up the sides, the new dimensions of the box will be $(x-8)$ cm in width, $(2x-8)$ cm in length, and $4$ cm in height. The volume of the box is given by $V = lwh = (x-8)(2x-8)(4) = 1120$. Solving this equation for $x$ gives $x = 18$ cm.

Solve the Problem 4 cm4 \mathrm {~cm}4 cm Squares from Each Corner and Folding Up the Sides

Solve the Problem $4 \mathrm {~cm}$ Squares from Each Corner and Folding Up the Sides