The areas of two similar triangles are 121 cm2 and 64 cm2 respectively.
Question:

The areas of two similar triangles are $121 \mathrm{~cm}^{2}$ and $64 \mathrm{~cm}^{2}$ respectively. If the median of the first triangle is $12.1 \mathrm{~cm}$, find the corresponding median of the other.

Solution:

Given: The area of two similar triangles is $121 \mathrm{~cm}^{2}$ and $64 \mathrm{~cm}^{2}$ respectively. IF the median of the first triangle is $12.1 \mathrm{~cm}$

To find: corresponding medians of the other triangle

We know that the ratio of areas of two similar triangles is equal to the ratio of squares of their medians.

$\frac{\operatorname{ar}(\text { triangle } 1)}{\operatorname{ar}(\text { triangle } 2)}=\left(\frac{\text { median } 1}{\text { median } 2}\right)^{2}$

$\frac{121}{64}=\left(\frac{12.1}{\text { median2 }}\right)^{2}$

taking squareroot on bothside

$\frac{11}{8}=\frac{12.1}{\text { median2 }}$

median $2=8.8 \mathrm{~cm}$

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