Answer:
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.
