The perimeter of a rectangle is 86 cm. The numbers representing its area and breadth are in the ratio of 9: 1, respectively. The breadth of the rectangle is:

34 cm

We know that,

Area of rectangle = Length × Breadth

Perimeter of rectangle = 2 (Length + Breadth)

Given that,

Perimeter = 86 cm

Ratio of Area and its breadth = 9 : 1

According to the question,

Area : Breadth = 9 : 1

=  \(\frac{(L × B) }{B}\) = \(\frac{9}{1}\)

= L = 9 cm

Now, Perimeter of rectangle = 86 = 2(9 + Breadth)

= 9 + Breadth = 43

= Breadth = 34 cm