Question

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

Answer 1

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