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Question
Sides of two similar triangles are in the ratio 4 : 9. Areas of these triangles are in the ratio.
Options
2 : 3
4 : 9
81 : 16
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.
`\text{ar(tringle 1)}/\text{ar(tringle 2)}=(\text{side1}/\text{side2})^2`
`=(4/6)^2`
`\text{ar(tringle 1)}/\text{ar(tringle 2)}=16/81`
Hence the correct answer is option `(d)`
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