Explanation:
l = length
b = breadth
l = b + 5
area = l × b = 594 m²
l = 594/b = b + 5
let's multiply both sides by b to get rid of the fraction :
594 = b² + 5b
b² + 5b - 594 = 0
remember how to solve a quadratic equation
0 = ax² + bx + c
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
x = b
a = 1
b = 5 (different b than the one that is equal to x).
c = -594
x = (-5 ± sqrt(5² - 4×1×-594))/(2×1) =
= (-5 ± sqrt(25 + 2376))/2 =
= (-5 ± sqrt(2401))/2 =
= (-5 ± 49)/2
x1 = (-5 + 49)/2 = 44/2 = 22
x2 = (-5 - 49)/2 = -54/2 = -27
a negative side length does not make any sense for a graphical object.
so, our solution for x (= the breadth of the hall) is 22 m.
and the length is then
l = b + 5 = 22 + 5 = 27 m.
perimeter = 2×l + 2×b = 2×27 + 2×22 = 54 + 44 = 98 m.