If the perimeter and length of a rectangle are in the ratio 6:1 and the area of the rectangle is 288 cm² . Find the length of the rectangle.

12 cm

The area of the rectangle = 288 cm²

The ratio of perimeter and breadth of a rectangle = 6 ∶ 1

We know that,

Area if rectangle = length × breadth

Perimeter = 2(length + breadth)

According to the question,

\(\frac{2(l + b)}{b}\)= \(\frac{6}{1}\)

= 2l + 2b = 6b

= 4b = 2l

⇒ \(\frac{l}{b}\)= \(\frac{2}{1}\)

Let, length = 2m,

 breadth = m  

Area of rectangle = (2m × m) = 288

= 2m² = 288

= m² = 144

= m = 12