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Question
If the perimeter of two similar triangles is in the ratio 2 : 3, what is the ratio of their sides?
Options
4 : 9
2 : 3
`sqrt(2)` : `sqrt(3)`
3 : 2
Solution
2 : 3
Explanation:
Let two similar triangles be ABC and DEF.
Since, the triangles are similar,
∴ `("Perimeter" (ΔABC))/("Perimeter" (ΔDEF)) = (AB)/(DE)`
According to the question,
`("Perimeter" (ΔABC))/("Perimeter" (ΔDEF)) = 2/3`
∴ `(AB)/(DE) = 2/3`
Thus, the ratio of sides is 2 : 3.
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