a. An expression for the area is : L * W = (8 + 2x) ( 10 + x + [3x - 1]) = (8 + 2x) (9 + 4x)
b. If the border is one inch, then x = 1, and we have :
[8 + 2(1)] * [ 9 + 4(1) ] = [ 10 ] * [13] = 130 in^2
c. We need to solve this :
(8 + 2x) ( 9 + 4x) = 165 simplify
8x^2 + 50x + 72 = 165 subtract 165 from both sides
8x^2 + 50x - 93 = 0 factor
[4x + 31] [ 2x -3 ] = 0
Setting the first factor to 0 produces a negattive value for x
Setting the second factor to 0, we have that
2x - 3 = 0 add 3 ro both sdes
2x = 3 divide both sides by 2
x = 3/2 inches = 1.5 inches
