Step-by-step explanation:
the area of a rectangle is
length × width = 300 ft²
length = width + 5
(width + 5) × width = 300
width² + 5×width = 300
width² + 5×width - 300 = 0
the general solution to such a quadratic equation is
width = (-b ± sqrt(b² - 4ac))/(2a)
in our case
a = 1
b = 5
c = -300
width = (-5 ± sqrt(5² - 4×1×-300))/(2×1) =
= (-5 ± sqrt(25 + 1200))/2 =
= (-5 ± sqrt(1225))/2 = (-5 ± 35)/2
width1 = (-5 + 35)/2 = 30/2 = 15 ft
width2 = (-5 - 35)/2 = -40/2 = -20 ft
negative lengths for an actual object don't make sense, so width = 15 ft is our solution.
length = width + 5 = 15 + 5 = 20 ft
