Explanation:
l = length
w = width
l = w + 10
l×w = 600 m²
now, using the identity of the first equation in the second equation
(w + 10)×w = 600
w² + 10w = 600
w² + 10w - 600 = 0
the general solution to such a squared equation is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
x = w
a = 1
b = 10
c = -600
w = (-10 ± sqrt(10² - 4×1×-600))/(2×1) =
= (-10 ± sqrt(100 + 2400))/2 = (-10 ± sqrt(2500))/2 =
= (-10 ± 50)/2 = -5 ± 25
w1 = -5 + 25 = 20 m
w2 = -5 - 25 = -30
the negative solution does not make any sense for side lengths. so, the only valid solution is w = 20 m.
l = w + 10 = 20 + 10 = 30 m
the length is 30 m.
the width is 20 m.