Question

If the ratio of the side lengths of two similar rectangular

Answer 1

Given:

Ratio of the side lengths of two similar rectangular prisms is $\dfrac{3}{5}$.

To find:

The ratio of their areas.

Solution:

If two figures are similar then their areas are proportional to the squares of their corresponding sides.

$\dfrac{A_1}{A_2}=\dfrac{s_1^2}{s_2^2}$

$\dfrac{A_1}{A_2}=\left(\dfrac{s_1}{s_2}\right)^2$           ...(i)

Where, $A_1,A_2$ are areas and $s_1,s_2$ are corresponding sides.

It is given that ratio of the side lengths of two similar rectangular prisms is $\dfrac{3}{5}$. It means, $\dfrac{s_1}{s_2}=\dfrac{3}{5}$.

Using (i), we get

$\dfrac{A_1}{A_2}=\left(\dfrac{3}{5}\right)^2$

$\dfrac{A_1}{A_2}=\dfrac{3^2}{5^2}$

$\dfrac{A_1}{A_2}=\dfrac{9}{25}$

Therefore, the ratio of their areas is $\dfrac{9}{25}$. It is also written as 9:25.