The perimeter and length of a rectangle are in the ratio of 8 : 1, and the area of the rectangle is 1323 cm². Find the length of the rectangle.

21 cm

We know that,

Perimeter of the rectangle = 2 (length + breadth)

Area of the rectangle = Length × Breadth

Given,

Ratio of perimeter and length of a rectangle = 8 : 1

Area of rectangle = 1323 cm²

Let the ratio of perimeter and length of a rectangle = 8a : a

Let length = a, then

2 × (a + breadth) = 8a

= a + breadth = 4a

= breadth = 4a - a

= breadth = 3a

Area of the rectangle = 1323

= a × 3a = 1323

= a² = 441

= a = 21