Question:
The areas of two similar triangles are 169 cm2 and 121 cm2 respectively. If the longest side of the larger triangle is 26 cm. find the longest side of the smaller triangle.
Solution:
It is given that the triangles are similar.
Therefore, the ratio of the areas of these triangles will be equal to the ratio of squares of their corresponding sides.
Let the longest side of smaller triangle be x cm.
$\frac{\text { ar(Larger triangle) }}{\operatorname{ar}(\text { Smaller triangle })}=\frac{\text { (Longest side of larger traingle) }^{2}}{\text { (Longest side of smaller traingle) }^{2}}$
$\Rightarrow \frac{169}{121}=\frac{26^{2}}{x^{2}}$
$\Rightarrow x=\sqrt{\frac{26 \times 26 \times 121}{169}}$
$=22$
Hence, the longest side of the smaller triangle is 22 cm.