Answer:
The required equation is [tex]L(L-6)=720[/tex] and the length is 30 inches and width is 24 inches.
Step-by-step explanation:
Given : A rectangular dog bed has an area of 720 square inches. The width of the bed is 6 inches shorter than the length.
To find : Create and solve for an equation, that represents the area of the bed, that can be used to determine the length and width of the bed ?
Solution :
Let the length be 'L' and width be 'W'.
The width of the bed is 6 inches shorter than the length.
i.e. [tex]W=L-6[/tex]
The area of the rectangular dog bed is [tex]A=L\times W[/tex]
Substitute the value,
[tex]720=L\times (L-6)[/tex]
[tex]L^2-6L-720=0[/tex]
[tex]L^2-30L+24L-720=0[/tex]
[tex]L(L-30)+24(L-30)=0[/tex]
[tex](L-30)(L+24)=0[/tex]
[tex]L=30,-24[/tex]
Reject L=-24 (as dimensions are not negative)
The length is 30 inches.
The width is 24 inches.
Therefore, the required equation is [tex]L(L-6)=720[/tex] and the length is 30 inches and width is 24 inches.
