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?

Solution

The lengths, the breadths, and the volumes of two cuboids are in the ratios of 4 : 5, 3 : 4, and 2 : 3, respectively.

Let's assume the lengths of cuboids are 4x and 5x respectively.

Let's assume the breadths of cuboids are 3y and 4y respectively.

Let's assume the volumes of cuboids are 2z and 3z respectively.

Let's assume the heights of cuboids are $$h_1$$ and $$h_2$$ respectively.

$$\frac{voume\ of\ first\ cuboid\ }{voume\ of\ \sec ond\ cuboid\ }\ =\ \frac{length \times breadth \times height}{length \times breadth \times height}$$
$$\frac{2z}{3z}\ =\ \frac{4x\times 3y \times h_1}{5x\times 4y \times h_2}$$
$$\frac{2}{3}\ =\ \frac{3h_1}{5h_2}$$
$$\frac{10}{9}=\frac{h_1}{h_2}$$

Ratio of their heights = 10:9