Explanation:
s = side length of the original square.
the area of a rectangle is
length × width
length = s + 5
width = s - 3
(s + 5)(s - 3) = 84
s² - 3s + 5s - 15 = 84
s² + 2s - 15 = 84
s² + 2s - 99 = 0
for a quadratic equation
ax² + bx + c = 0
the general solution is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
x = s
a = 1
b = 2
c - -99
s = (-2 ± sqrt(2² - 4×1×-99))/(2×1) =
= (-2 ± sqrt(4 + 396))/2 =
= (-2 ± sqrt(400))/2 = (-2 ± 20)/2 =
= -1 ± 10
s1 = -1 + 10 = 9 ft
s2 = -1 - 10 = -11 ft
a negative solution for an actual length does not make any sense. so, s = 9 ft is our solution.
the perimeter of the original square was then
4 × 9 = 36 ft