Answer:
length is 20 meters
width is 12 meters
Explanation:
x = length
y = width
x = 2y - 4
x×y = 240
using the first equation as substitute in the second equation we get
(2y - 4)×y = 240
2y² - 4y - 240 = 0
the solution to such a quadratic equation is
x = (-b ± sqrt(b² - 4ac))/(2a)
here we are going for y instead of x, but it is the same principle.
a = 2
b = -4
c = -240
y = (4 ± sqrt(16 - 4×2×-240))/4 = (4 ± sqrt(16 + 1920))/4 =
= (4 ± sqrt(1936))/4 = (4 ± 44)/4 = (1 ± 11)
y1 = 1 + 11 = 12
y2 = 1 - 11 = -10
negative side lengths don't make any sense, so, y = 12 meters remains.
x = 2y - 4 = 2×12 - 4 = 24 - 4 = 20 meters