The area of two similar triangles are $36 \mathrm{~cm}^{2}$ and $100 \mathrm{~cm}^{2}$. If the length of a side of the smaller triangle in $3 \mathrm{~cm}$, find the length of the corresponding side of the larger triangle.
Since the ratio of areas of two similar triangles is equal to the ratio of the squares of any two corresponding sides.
$\frac{\text { Area of smaller triangle }}{\text { Area of larger triangle }}=\frac{(\text { Corresponding side of smaller triangle })^{2}}{(\text { Corresponding side of larger triangle })^{2}}$
$\frac{36}{100}=\frac{3^{2}}{(\text { Corresponding side of larger triangle })^{2}}$
(Corresponding side of larger triangle) $^{2}=\frac{9 \times 100}{36}$
(Corresponding side of larger triangle) $^{2}=\frac{100}{4}$
(Corresponding side of larger triangle) $^{2}=25$
$\Rightarrow$ Corresponding side of larger triangle $=5$
Hence, the length of the corresponding side of the larger triangle is $5 \mathrm{~cm}$
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