1) Let x=width ; 2x+3=length
Given: A=160m²
[tex]A = x(2x+3)[/tex]
[tex]160 = x(2x+3)
160 = 2x^2+3x
0 = 2x^2+3x -160
[/tex]
Using the quadratic formula you will get [tex]x = \frac{-3+\sqrt{1289} }{4} [/tex]
Therefore, length=[tex]\boxed{ \frac{3+ \sqrt{1289} }{2}m}[/tex]
2) Let x=width ; 3x+3=length
Given: A=126 ft²
[tex]A=x(3x+3)[/tex]
[tex]126 = x(3x+3)
126 = 3x^2 + 3x
42 = x^2 +x
0 = x^2 +x -42
0 = (x+7)(x-6)
x = -7 ; x = 6[/tex]
Use x=6 ; Therefore, [tex]\boxed{length=21 ft}[/tex]
3) Rate of Kenneth = [tex] \frac{1}{x} [/tex]
Rate of Mario = [tex] \frac{1}{x-20} [/tex]
[tex] \frac{90}{x} + \frac{90}{x-20} =1[/tex]
[tex] \frac{90x-1800+90x}{x(x-20)}=1 [/tex]
