Final answer:
To determine the width 'x' of the border, solve the quadratic equation derived from setting the total area of the border equal to 144 square inches and subtracting the area of the original rectangle (14*18) from the area of the expanded rectangle including the border.
Step-by-step explanation:
The student is asking how to find the width of a border that needs to fit around a rectangular board while having an area of 144 square inches. First, to address this problem, we denote the width of the border as 'x'. Since the original rectangle is 14 inches by 18 inches, the new dimensions of the larger rectangle, once the border is included, become '14 + 2x' by '18 + 2x'. Next, we calculate the new area of the larger rectangle and subtract the area of the original rectangle to equate it to the area of the border which is given as 144 square inches.
Let's solve the equation:
(14 + 2x)(18 + 2x) - 14*18 = 144.
Simplifying this we get a quadratic equation which we solve for 'x' to find the width of the border.