Marie has a rectangular board 12 inches by 16 inches around which she wants to put a uniform border of sherlls. if she has enough shells for a border whose area is 128 determine the width of the border

Area of rectangular board = length (inches) x width (inches) = 12" x 16" = 192 in²

Area of the border is given as 128 in²

Adding the area of the board and the border gives (192 + 128)in² = 320 in²

Set this up as the algebraic equation (x + 12)(x + 16) = 320 and solve for x:

Remember to use the FOIL method, which is multiplying the terms in the order of first, outer, inner, last.

x² + 12x + 16x + 192 = 320

x² + 28x + 192 - 320 = 0

x² + 28x - 128 = 0

solve for the two x values:

(x + 32)(x - 4) = 0, and knowing we only need the positive x value

x = 4 or 4 inches is the width of the border