Question

A playing card has a perimeter of 28 centimeters. Its area is 45 square centimeters. What are the dimensions of the playing card?

Answer 1

Explanation:

A playing card is in the form of a rectangle whose perimeter is equal to 28 cm and area is 45 cm².

If l and b are length and breadth of the rectangle.

Area,

`A=lb`

`45=lb\\\\l=(45)/(b)\ .....(1)`

Perimeter,

`P=2(l+b)\\\\28=2(l+b)\\\\14=(l+b)\ ....(2)`

Put the value of l from equation (1) to equation (2). So,

`14=(45)/(b)+b\\\\14=(45+b^2)/(b)\\\\14b=45+b^2\\\\b^2-14b+45=0\\\\b^2-9b-5b+45=0\\\\b(b-9)-5(b-9)=0\\\\b=5\ cm, 9\ cm`

Put the value of b in equation (1),

If b = 5 cm

`l=(45)/(5)=9\ cm`

If b = 9 cm

`l=(45)/(9)=5\ cm`

So, the dimensions of the playing card is 9 cm by 5 cm.