Explanation:
l = length
w = width
l = 2w + 5
l × w = 63
using the identity of the first equation in the second :
(2w + 5) × w = 63
2w² + 5w = 63
2w² + 5w - 63 = 0
the general solution to such a squared equation is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
x = w
a = 2
b = 5
c = -63
w = (-5 ± sqrt(5² - 4×2×-63))/(2×2) =
= (-5 ± sqrt(25 + 504))/4 = (-5 ± sqrt(529))/4 =
= (-5 ± 23)/4
w1 = (-5 + 23)/4 = 18/4 = 4.5 ft
we = (-5 - 23)/4 = -28/4 = -7
a negative Stilton does not make any sense for a side length, so, the only valid solution is w = 4.5 ft.
l = 2w + 5 = 2×4.5 + 5 = 9 + 5 = 14 ft
so,
the length = 14 ft
the width = 4.5 ft