Step-by-step explanation:
it is a rectangle (usually).
so,
2×length + 2×width = 80
therefore, length + width = 40
length×width = 384
length = 384/width
384/width + width = 40
384 + width² = 40×width
width² - 40×width + 384 = 0
the general solution for such a square equation is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
x = width
a = 1
b = -40
c = 384
width = (40 ± sqrt((-40)² - 4×1×384))/(2×1) =
= (40 ± sqrt(1600 - 1536))/2 =
= (40 ± sqrt(64))/2 = (40 ± 8)/2 =
= 20 ± 4
width1 = 20 + 4 = 24 cm
length1 = 40 - 24 = 16 cm
width2 = 20 - 4 = 16 cm
length2 = 40 - 16 = 24 cm
so, both solutions are the same.
the greeting card is 24×16 cm. or 16×24, depending on how you are holding it.
