Question

A rectangular piece of cardboard is 15 inches longer than it is wide. A 5-inch square is cut from each corner, and the remaining piece is folded to form a box. If the volume of the box is 1,250 cubic inches, what is the length of the box?
A.25 inches
B.30 inches
C.35 inches
D.40 inches

Answer 1

Let x be the width of the cardboard, then the length is x+15. If 5 unches square is cut from each corner, then the new length is x+15-5·2=x+5 and the new width is x-5·2=x-10. The height of the formed box is 5 in. Now you can find the box volume:

$V=\text{ width }\cdot \text{ length }\cdot \text{ height },\\ V=(x-10)\cdot (x+5)\cdot 5,\\ V=5(x^2-5x-50)$.

If the volume of the box is 1,250 cubic inches, then

$5(x^2-5x-50)=1250,\\ x^2-5x-50=250,\\ x^2-5x-300=0,\\ D=(-5)^2-4\cdot (-300)=25+1200=1225,\\ \sqrt{D} =35,\\ x_{1,2}=\dfrac{5\pm 35}{2} =20,-15$.

The length of the box is x+5=20+5=25 in. (the negative x is extra, because the length couldn't be negative).

Answer: the length of the box is 25 inches.