Question

The playing surfaces of two foosball tables are similar. The ratio of the corresponding side lengths is $10:7$. What is the ratio of the areas?

Answer 1

Find the ratio of the areas.

Given, The ratio of the corresponding side lengths is $10:7$.

Since, when two figures are similar, then

$\Rightarrow \frac{AreaoffigureA}{AreaoffigureB}={\left(\frac{SidelengthoffigureA}{SidelengthoffigureB}\right)}^2$

So, the ratio of the areas of foosballs is

$$\begin{gathered} \Rightarrow \frac{AreaoffigureA}{AreaoffigureB}={\left(\frac{10}{7}\right)}^2 \\ \Rightarrow \frac{AreaoffigureA}{AreaoffigureB}=\frac{100}{49} \end{gathered}$$

Hence, the ratio of area of two foosball is $\frac{100}{49}$.