Question

The volume of a rectangular solid can be written as V=LWH, where L is the length of the solid, W is the width, and H is the height. A box of cereal has a width of 2 inches. It’s height is 2 inches longer than it’s length. If the volume of the box is 198 cubic inches, what are the length and height of the box ?

Answer 1

Answer:

The length of the rectangle is 9 inches.

The height of the rectangle is 11 inches.

Step-by-step explanation:

Given : The volume of a rectangular solid can be written as V=LWH, where L is the length of the solid, W is the width, and H is the height. A box of cereal has a width of 2 inches. It’s height is 2 inches longer than it’s length. If the volume of the box is 198 cubic inches.

To find : What are the length and height of the box ?

Solution :

The width of the box is L inches

The width of the box is W=2 inches

The height is 2 inches longer than it’s length i.e H=L+2

The volume of a rectangular solid is $V=L\times W\times H$

$198=L\times 2\times (L+2)$

$99=L^2+2L$

$L^2+2L-99=0$

$L^2+11L-9L-99=0$

$L(L+11)-9(L+11)=0$

$(L+11)(L-9)=0$

$L=-11,9$

Reject L=-11 as dimension cannot be negative.

The length of the rectangle is 9 inches.

The height of the rectangle is 11 inches.