The areas of two similar triangles are $121\ cm^2$ and $64\ cm^2$ respectively. If the median of the first triangle is $12.1\ cm$, find the corresponding median of the other.
Given:
The areas of two similar triangles are $121\ cm^2$ and $64\ cm^2$ respectively.
The median of the first triangle is $12.1\ cm$.
To do:
We have to find the corresponding median of the other triangle.
Solution:
We know that,
The ratio of the areas of the two similar triangles is equal to the ratio of the squares of their medians.
Therefore,
$\frac{area\ of\ first\ triangle}{area\ of\ second\ triangle} = (\frac{median\ of\ first\ triangle}{median\ of\ second\ triangle})^2$
$\frac{121}{64} = (\frac{12.1}{median\ of\ second\ triangle})^2$
$\frac{median\ of\ second\ triangle}{12.1}=\sqrt{\frac{64}{121}}$
$median\ of\ second\ triangle = \frac{12.1\times8}{11}$
$median\ of\ second\ triangle=1.1 \times 8$
$median\ of\ second\ triangle=8.8\ cm$
The median of the other triangle is $8.8\ cm$.
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