Let the length = x and the width = y
For the length of fence we have x +x + y = 48 = 2x +y = 48
Rewrite as y = 48 - 2x
For the area we have x * y = 254
Replace y in the are equation:
x * 48 -2x = 254
Simplify the left side:
48x - 2x^2 = 254
Subtract 254 from both sides:
48x - 2x^2 - 254 = 0
Using the quadratic formula solve for x:
a = -2, b = 48 and c = -254
x = -48 + 4√17/-4
x = 16.123 m.
The length = x = 16.123 meters.
The width = 48 - (16.123*2) = 15.754 meters
Rounding to the nearest centimeter:
Length = 16.1 ( 16 meters and 1 cm)
Width = 15.8 ( 15 meters and 8 cm)