Ineed with these quadratic applications.

1. d

2. c

Step-by-step explanation:

1. "You have a 12in by 14in picture you framed.  When you hung the picture, you found that the area is 261.44 square inches.  What is the width of the frame?"

If we call the width of the frame x, then the total width is w = 12 + 2x, and the total height is 14 + 2x.  Area is width times height, so:

A = wh

261.44 = (12 + 2x) (14 + 2x)

Distribute using FOIL (first outer inner last):

261.44 = 12×14 + 12×2x + 2x×14 + 2x×2x

261.44 = 168 + 24x + 28x + 4x²

261.44 = 168 + 52x + 4x²

0 = 4x² + 52x − 93.44

0 = x² + 13x − 23.36

Solve with quadratic formula:

x = [ -b ± √(b² − 4ac) ] / 2a

x = [ -13 ± √(169 + 93.44) ] / 2

x = (-13 ± 16.2) / 2

x = 1.6 or -14.6

Since x must be positive, x = 1.6 inches.

2. "A flower garden has been design with an L shaped walkway and viewing area around two sides as shown.  The garden itself is 5 yards by 8 yards.  The total area needed to build this landscape design is 60.9525 square yards.  What is the width of the walkway?"

If we call the width of the walkway x, then the total width is w = 5 + x and the total length is l = 8 + x.  Area is width times length, so:

A = wl

60.9525 = (5 + x) (8 + x)

Distribute using FOIL (first outer inner last):

60.9525 = 5×8 + 5×x + x×8 + x×x

60.9525 = 40 + 5x + 8x + x²

60.9525 = 40 + 13x + x²

0 = x² + 13x − 20.9525

Solve with quadratic formula:

x = [ -b ± √(b² − 4ac) ] / 2a

x = [ -13 ± √(169 + 83.81) ] / 2

x = (-13 ± 15.9) / 2

x = 1.45 or -14.45

Since x must be positive, x = 1.45 yards.