Step-by-step explanation:
length × width = 24
2×length + 2×width = 22
length + width = 11
length = 11 - width
this we use in the first equation again :
(11 - width) × width = 24
11×width - width² = 24
width² - 11×width + 24 = 0
the general solution to an quadratic equation :
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
x = width
a = 1
b = -11
c = 24
and so we get
width = (11 ± sqrt((-11)² - 4×1×24))/2×1) =
= (11 ± sqrt(11² - 96))/2 = (11 ± sqrt(121-96))/2 =
= (11 ± sqrt(25))/2 = (11 ± 5)/2
width1 = (11 + 5)/2 = 16/2 = 8 cm
width2 = (11 - 5)/2 = 6/2 = 3 cm
and teenaged to this is then
length1 = 11 - width1 = 11 - 8 = 3 cm
length2 = 11 - width2 = 11 - 3 = 8 cm
so, it is clear. one dimension has to be 8 cm, and the other one 3 cm. it does not matter which is which.
