If the perimeter of a rectangle is 30 cm and the area is 54 square cm,

Question

then what are the dimensions of the rectangle?

Answer 1

Let the length and width of rectangle = l , w .

Perimeter of rectangle = 2 ( l + w ) = 30 cm

2 ( l + w ) = 30---> (1)

Area of rectangle  = lw  = 54 cm^2

l = 54/w  ---> (2)

substitute the l  value in equation (1).

2( 54/w  + w  ) = 30

108/w  + 2w  = 30

(108 + 2w ^2) / w  = 30

2w ^2 + 108 = 30w

2w ^2 - 30w + 108 = 0

w ^2 - 15w  + 54 = 0

w ^2 - 9w  - 6w  + 54 = 0

w ( w  - 9) - 6(w  - 9) = 0

( w  - 9) ( w  - 6) = 0

Apply zero product property.

( w  - 9) = 0 and ( w  - 6) = 0

w  = 9 and w  = 6

From equation (2)

For w  = 9 then l  = 6

For w  = 6 then l  = 9

Dimensions of rectangle are 9cm and 6 cm.