Question

Area of two similar triangles are $36c{m}^2$ and $100c{m}^2$. If the length of a side of the larger triangle is $20cm$, find the length of the corresponding of the smaller triangle.

Answer 1

Here, $ar\left(\Delta ABC\right)=36c{m}^2.ar\left(\Delta DEF\right)=100c{m}^2,DE=20cm,AB=?$

If $\Delta ABC\sim \Delta DEF$, then by area theorem $\frac{ar\left(\Delta ABC\right)}{ar\left(\Delta DEF\right)}={\left(\frac{AB}{DE}\right)}^2$

$\frac{36}{100}={\left(\frac{AB}{DE}\right)}^2$

$\frac{6}{10}=\left(\frac{AB}{DE}\right)$ [Taking square root]

or $\frac{6}{10}=\frac{AB}{20}$

$\Rightarrow AB=\frac{6\times 20}{10}=12cm$

$\therefore AB=12cm$. Hence, side of smaller $\Delta$ is $12cm$