Question

A playing card has an area of 50 square centimeters and a perimeter of 30 centimeters. What are the dimensions of the playing card?

Answer 1

The dimensions of playing card is L = 10 centimeter and W=5 centimeter, If the playing card has an area of 50 square centimeter and a perimeter of 30 centimeters.

Explanation:

The given is,

Playing card has an area of 50 square centimeters

A perimeter of 30 centimeters

Step:1

A playing card is in the shape of rectangle,

Formula for perimeter of rectangle is,

`Perimeter, P = 2(l+w)` .........................(1)

Formula for area of rectangle is,

`Area, A= lw`......................................(2)

Where, l - Length of rectangle

w - Width of rectangle

Step:2

From the given values equation (1) becomes,

`30 = 2(l+w)`

`(30)/(2)=(l+w)`

`15 =(l+w)`

`w=15-l` .............................(3)

Width value in terms of length is calculated.

Step:2

Equation (2) becomes,

`50 = (15-l)(l)`

`50= 15l -l^(2)`

`l^(2)-15l+50=0`

Solving the above equation,

`=10`

`l=10 cm`

Step:3

Equation (3) becomes,

`w=15-l`

`=15-10`

`=5`

w = 5 cm

Result:

The dimensions of playing card is L = 10 centimeter and W = 5 centimeter, If the playing card has an area of 50 square centimeter and a perimeter of 30 centimeters.