The ratio of two sides of a rectangle are in the ratio 4 : 7.  If its perimeter is 154 cm, then find length of its diagonal.

56 cm

Ratio of length to breadth = 4 : 7

l + b = 11x

ATQ, 

Perimeter = 2(l+b) = 154

⇒ 22x = 154

       x = 7

Sides of rectangle = 4 × 7 and 7 × 7 = 28 & 49

Diagonal = \(\sqrt {28^2 + 49^2}\)

             = 7\(\sqrt {16 + 49}\)

             = 7\(\sqrt {65}\) = 7 × 8 = 56 cm (approx)