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 [tex]V=L\times W\times H[/tex]
[tex]198=L\times 2\times (L+2)[/tex]
[tex]99=L^2+2L[/tex]
[tex]L^2+2L-99=0[/tex]
[tex]L^2+11L-9L-99=0[/tex]
[tex]L(L+11)-9(L+11)=0[/tex]
[tex](L+11)(L-9)=0[/tex]
[tex]L=-11,9[/tex]
Reject L=-11 as dimension cannot be negative.
The length of the rectangle is 9 inches.
The height of the rectangle is 11 inches.
