The perimeter of a playing card is 28 centimeters. The area is 48 square centimeters. What are the dimensions of the playing card?

Let length be l

and breadth be b

perimeter = 28

2 (l+b) = 28

l + b = 14

l = 14 - b

area = 48

l x b = 48

(14 - b) b = 48

14b - b^2 = 48

b^2 - 14b + 48 = 0

b^2 - 6b - 8b + 48 = 0

b (b - 6) - 8 (b - 6) = 0

(b-8) (b-6) = 0

so

either b = 8 or b = 6

if b = 8

l = 14 - 8 = 6

(not possible as length cannot be smaller than breadth)

so

breadth = 6

length = 8