Find the value of the ratio (red to blue) of the areas of the similar figures.

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Solution

Find the ratio of the areas of figures.
Given, figure
From figure, we can have that
The side length of red triangle is $4 units$ .
The side length of blue triangles is $15 units$ .
Since, we know that when two figures are similar then the value of the ratio of their perimeter is equal to the value of the ratio of their corresponding side lengths
$\Rightarrow \frac{A r e a o f r e d f i g u r e}{A r e a o f b l u e f i g u r e} = \frac{{(S i d e l e n g t h o f r e d f i g u r e)}^{2}}{{(S i d e l e n g t h o f b l u e f i g u r e)}^{2}}$
So, the ratio of area of red figure to the blue figure is
$\Rightarrow \frac{A r e a o f r e d f i g u r e}{A r e a o f b l u e f i g u r e} = \frac{{(S i d e l e n g t h o f r e d f i g u r e)}^{2}}{{(S i d e l e n g t h o f b l u e f i g u r e)}^{2}} \Rightarrow \frac{A r e a o f r e d f i g u r e}{A r e a o f b l u e f i g u r e} = \frac{4^{2}}{15^{2}} = \frac{16}{225}$
Hence, the ratio of area of red figure to the blue figure is $\frac{16}{225}$ .

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