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similar triangles

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similar triangles

by rahul.s » Tue Feb 09, 2010 8:04 am
2 similar triangles have areas in the ratio of 9:1. what is the ratio of these triangles' perimeters?

[spoiler]OA is 3:1[/spoiler]
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by ajith » Tue Feb 09, 2010 8:15 am
rahul.s wrote:2 similar triangles have areas in the ratio of 9:1. what is the ratio of these triangles' perimeters?

[spoiler]OA is 3:1[/spoiler]
If the similarity ratio of two similar triangles is a : b, then the ratio of their areas is a^2 : b^2

The converse is also true

so the sides are in the ration 1:3

and the ration of perimeter which is sum of sides is also 1:3
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by rahul.s » Tue Feb 09, 2010 8:23 am
so the ratio of the perimeter is sqrt9 : sqrt1, which is 3:1. is that right?
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by ajith » Tue Feb 09, 2010 8:25 am
rahul.s wrote:so the ratio of the perimeter is sqrt9 : sqrt1, which is 3:1. is that right?
That is right Rahul
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by shashank.ism » Tue Feb 09, 2010 10:57 am
rahul.s wrote:2 similar triangles have areas in the ratio of 9:1. what is the ratio of these triangles' perimeters?

[spoiler]OA is 3:1[/spoiler]
since the area is in ratio 9:1
so sides are in ratio 3:1
perimeter is proportional to side as it is sum of sides so its ratio = 3:1
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by shashank.ism » Tue Feb 09, 2010 10:58 am
rahul.s wrote:so the ratio of the perimeter is sqrt9 : sqrt1, which is 3:1. is that right?
3:1 is absolutely right rahul, always area would be square of the sides or perimeter..
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by harsh.champ » Tue Feb 09, 2010 1:10 pm
rahul.s wrote:2 similar triangles have areas in the ratio of 9:1. what is the ratio of these triangles' perimeters?

[spoiler]OA is 3:1[/spoiler]
We know that the area = 1/2 x base x altitude.

So, we have 2 sides over here.

If the areas are i the ratio 9:1,then the sides are in the ratio 3:1 as is evident by the upper equation.
[For example consider a rt.< triangle]

Hence, perimeters will bw in the ratio 9:3 which is equal to 3:1.
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