Explanation:
the area of a rectangle is
length × width
in our case
length × width = 112 m²
and we know
width = length - 6
when using this in the first area equation we get
length × (length - 6) = 112
length² - 6×length = 112
length² - 6×length - 112 = 0
we know that for a general quadratic equation
ax² + bx + c = 0
the solution is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
x = length
a = 1
b = -6
c = -112
length = (6 ± sqrt((-6)² - 4×1×-112))/(2×1) =
= (6 ± sqrt(36 + 448))/2 = (6 ± sqrt(484))/2 =
= (6 ± 22))/2 = 3 ± 11
length 1 = 3 + 11 = 14 m
length 2 = 3 - 11 = -8 m
a negative number does not make any sense for an actual length, so length 1 is the solution.
length = 14 m
width = length - 6 = 14 - 6 = 8 m