The area of a rectangle is 180 cm$^2$ If the ratio of length and breadth of the rectangle is 5 : 4, then what is the length (in cm)of diagonal of the rectangle?

$\sqrt{369}$

We have,

Area of rectangle = 180 cm².

Ratio of Length and Breadth of the rectangle = 5 : 6.

Let, Length = 5x

Breadth = 4x

According to question,

5x × 4x = 180

= 20x² = 180

= x² = 9

= x = 3

Length = 5 × 3 = 15cm

Breadth = 4 × 3 = 12cm

= The diagonal of rectangle =\(\sqrt {(15^2 + 12^2) }\) = \(\sqrt {369}\)