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Sides of two similar triangles are in the ratio 4:9. Areas of these triangles are in the ratio
(a) 2:3
(b) 4:9
(c) 81:16
(d) 16:81
Given:
Sides of two similar triangles are in the ratio 4:9.
To do:
We have to find the ratio of the areas of these triangles.
Solution:
We know that,
If two triangles are similar, then the ratio of the area of both triangles is proportional to the square of the ratio of their corresponding sides.
Therefore,
Ratio of the areas of triangles $=(\frac{4}{9})^{2}$
$=\frac{16}{81}$
The ratio of the areas of the given triangles is $16:81$.
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