Answer:
length = 23 inches; width = 18 inches.
Step-by-step explanation:
Length and width are found from their expressions after solving for x. The value of x can be found from ...
... overall area - cutout area = 148 . . . . . . square inches
... (2x -1)(x +6) - (2x -5)(x +2) = 148 . . . . . substitute length and width expressions. Each area is the product of length and width.
... 2x² +11x -6 -(2x² -x -10) = 148 . . . . . . . multiply binomials
... 12x +4 = 148 . . . . collect terms
... 12x = 144 . . . . . . . subtract 4
... x = 12 . . . . . . . . . . divide by 12
Then the overall length is ...
... 2x -1 = 2·12 -1 = 23 . . . inches
and the overall width is ...
... x +6 = 12 +6 = 18 . . . inches
The overall dimensions of the original mat are 23 inches by 18 inches.
