Question

Cruz's Frame shop makes. a mat by cutting out the inside of a rectangular mat board. Find the length and width of the original mat if the area of the mat board is 148 square inches. the outside length and with are 2x-1 and x+6 the inside length and width are 2x-5 and x+2

Answer 1

length = 23 inches; width = 18 inches.

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.