Question:
Sides of two similar triangles are in the ratio 4 : 9. Areas of these triangles are in the ratio.
(a) $2: 3$
(b) $4: 9$
(c) $81: 16$
(d) $16: 81$
Solution:
Given: Sides of two similar triangles are in the ratio 4:9
To find: Ratio of area of these triangles
We know that the ratio of areas of two similar triangles is equal to the ratio of squares of their corresponding sides.
$\frac{\operatorname{ar}(\text { triangle } 1)}{\operatorname{ar}(\text { triangle } 2)}=\left(\frac{\operatorname{side} 1}{\operatorname{side} 2}\right)^{2}$
$=\left(\frac{4}{9}\right)^{2}$
$\frac{\operatorname{ar}(\text { triangle } 1)}{\operatorname{ar}(\text { triangle } 2)}=\frac{16}{81}$
Hence the correct answer is option d