Answer:
A. 28.23 inches
Step-by-step explanation:
Since the are of the old and new flower bed are the same,
[tex]A_{old}[/tex] = [tex]A_{new}[/tex]
l(l- 14) = (l- 22)(2l+ 8)
[tex]l^{2}[/tex]- 14l = 2[tex]l^{2}[/tex] +8l -44l -176
[tex]l^{2}[/tex]- 14l = 2[tex]l^{2}[/tex] -36l -176
combining the terms to form a quadratic equation;
[tex]l^{2}[/tex] - 2[tex]l^{2}[/tex] -14l +36l +176 = 0
-[tex]l^{2}[/tex] +22l + 176 = 0
multiply through by minus sign;
[tex]l^{2}[/tex] -22l - 176 = 0
Applying the quadratic formula,
[tex]\frac{-b }{2}[/tex] ± [tex]\sqrt{b^{2} - 4ac }[/tex]
a = 1, b= -22 and c = -176
substitute these values in the equation,
= [tex]\frac{22}{2}[/tex] ±[tex]\sqrt{484 + 704}[/tex]
= 28.233688
= 28.23 inches
