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

length = 23 inches; width = 18 inches.

Step-by-step explanation:

Length and width can be found from the following expression after solving for x. The expression is given by:

outside area - inside area = 148 square inches

(2·x - 1) · (x + 6) - (2·x - 5) · (x + 2) = 148 (On substitute length and width expressions. Each area is the product of length and width.)

⇒ 2·x² + 11·x - 6 - (2·x² - x - 10) = 148

⇒ 12·x + 4 = 148 ... (On simplifying the expression)

⇒ 12·x = 144

⇒ x = 12

Then the original length of the mat is given by substituting value of x in outside length expression:

2·x - 1 = 2·12 - 1 = 23 inches

and the original width of the mat is given by:

x + 6 = 12 + 6 = 18 inches

Hence, the overall dimensions of the original mat are 23 inches by 18 inches.