Answer:
7 ft
Step-by-step explanation:
the area of a rectangle is
length × width
in our case
length × width = 105 ft²
and we know
length = width + 8
that identity we can use in the area equation and get
(width + 8) × width = 105
width² + 8width = 105
width² + 8width - 105 = 0
and that is how your teacher got the equation
w² + 8w - 105 = 0
the general solution for such a quadratic equation is
w = (-b ± sqrt(b² - 4ac))/(2a)
with our equation
a = 1
b = 8
c = -105
w = (-8 ± sqrt(8² - 4×1×-105))/(2×1) =
= (-8 ± sqrt(64 + 420))/2 = (-8 ± sqrt(484))/2 =
= (-8 ± 22)/2 = -4 ± 11
w1 = -4 + 11 = 7
w2 = -4 - 11 = -15
negative values/ solutions for side lengths of shapes don't make sense, so the only valid solution is w = 7 ft
