**Question:**

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.

**Solution:**

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 $5 \mathrm{~cm}$