similar triangles

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rahul.s: Master | Next Rank: 500 Posts; Posts: 324; Joined: Thu Dec 24, 2009 6:29 amFollowed by: 1 member; Thanked: 17 times

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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ajith: Legendary Member; Posts: 1275; Joined: Thu Sep 21, 2006 11:13 pmFollowed by: 2 members; Location: Arabian Sea; Thanked: 125 times

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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rahul.s: Master | Next Rank: 500 Posts; Posts: 324; Joined: Thu Dec 24, 2009 6:29 amFollowed by: 1 member; Thanked: 17 times

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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ajith: Legendary Member; Posts: 1275; Joined: Thu Sep 21, 2006 11:13 pmFollowed by: 2 members; Location: Arabian Sea; Thanked: 125 times

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

Always borrow money from a pessimist, he doesn't expect to be paid back.

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shashank.ism: Legendary Member; Posts: 1022; Joined: Mon Jul 20, 2009 11:49 pmFollowed by: 2 members; Location: Gandhinagar; Thanked: 41 times

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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shashank.ism: Legendary Member; Posts: 1022; Joined: Mon Jul 20, 2009 11:49 pmFollowed by: 2 members; Location: Gandhinagar; Thanked: 41 times

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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harsh.champ: Legendary Member; Posts: 1132; Joined: Mon Jul 20, 2009 3:38 amFollowed by: 6 members; Location: India; Thanked: 64 times; GMAT Score:760

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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