The lengths, the breadths, and the volumes of two cuboids are in the ratios of 4 : 5, 3: 4, and 2 : 3, respectively. What is the ratio of their heights?

10 : 9

We know that,

Area of a cuboid = length × breadth × height

We have,

Ratio of the length = 4 : 5

Ratio of the breadth = 3 : 4

Ratio of the volume = 2 : 3

Now according to the question,

\(\frac{4 × 3 × h}{5 × 4 × H}\) = \(\frac{2}{3}\)  

\(\frac{12 × h}{20 × H}\) = \(\frac{2}{3}\) 

\(\frac{ h}{ H}\) = \(\frac{10}{9}\)