Question

A greeting card has a perimeter of 80 cm and an area of 384 square cm what are the dimensions for the greeting card

Answer 1

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.