Sides of two similar triangles are in the ratio 4 : 9. Areas of these triangles are in the ratio.
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

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