Answer:
Width is 19.24 ft and length is 24.24 ft
Step-by-step explanation:
Step 1: Write an equation
[tex]A = l * w[/tex]
[tex]505\ ft^2 = (7+w) * w[/tex]
[tex]505\ ft^2 = (w*w) + (w*7)[/tex]
[tex]505\ ft^2 - 505\ ft^2 = w^2 + 7w - 505\ ft^2[/tex]
[tex]0= w^2 + 7w - 505\ ft^2[/tex]
Step 2: Determine the dimensions
Use Quadratic formula
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
[tex]x=\frac{-7\pm\sqrt{(7)^2-4(1)(-505)}}{2(1)}[/tex]
[tex]x=\frac{-7\pm\sqrt{2069}}{2}[/tex]
[tex]x = \frac{-7\pm45.486}{2}[/tex]
[tex]x=19.24,\ -26.24[/tex]
Since length cannot be negative, we will use 19.24 for x.
Step 3: Determine the length
[tex]l = w + 5[/tex]
[tex]l = 19.24 + 5[/tex]
[tex]l = 24.24[/tex]
Answer: Width is 19.24 ft and length is 24.24 ft
