Question

Area of two similar triangle are $144{\text{cm}}^2$ and $81{\text{cm}}^2$. If one side of the first triangle is $6\text{cm}$, then find the corresponding side of the second triangle.

Answer 1

Area of similar triangles are $144{\text{cm}}^2$ and $81{\text{cm}}^2$

Since one side of the triangle is $6\text{cm}$,

Hence the other corresponding side be $x$ and can be find out by the following theorem;

$\frac{ar\left({△}_1\right)}{ar\left({△}_2\right)}={\left(\frac{s_1}{s_2}\right)}^2$

where, $s_1,s_2$ are the corresponding sides of similar triangles

$\Rightarrow \frac{144}{81}={\left(\frac{6}{x}\right)}^2\Rightarrow x=4.5\text{cm}$