Geometry DS

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kop: Junior | Next Rank: 30 Posts; Posts: 29; Joined: Thu Oct 03, 2013 11:35 am; Thanked: 1 times

by kop » Wed Nov 20, 2013 1:01 am

Triangles ABC and DEF are similar. What percent of the area of triangle DEF is triangle ABC?

1. Sides AB and DE connect similar angles, and AB is 3 times DE.
2. Side AB = 9

Somebody Please explain me similar triangles properties.
Here to calculate the area we need height?? But how do we get height from the above information?

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Source: Beat The GMAT — Data Sufficiency | Wed Nov 20, 2013 1:01 am

pareekbharat86: Master | Next Rank: 500 Posts; Posts: 168; Joined: Thu Nov 01, 2012 7:43 pm; Thanked: 1 times

by pareekbharat86 » Wed Nov 20, 2013 4:38 am

2 or more triangles are similar to each other if-

1. If internal angles of the triangles are congruent (AAA) or
2. If all three pairs of corresponding sides are in the same proportion (SSS) or
3. If 2 pairs of sides are in the same proportion and the included angle is equal (SAS).

One of the properties of the similar triangles (say ABC and DEF) is,

area of ABC/area of DEF= square of (length of any one side of ABC/length of corresponding side of DEF)

Try using the above to solve the ques.

Thanks,
Bharat.

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Uva@90: Master | Next Rank: 500 Posts; Posts: 490; Joined: Thu Jul 04, 2013 7:30 amFollowed by: 5 members; Location: Chennai, India; Thanked: 83 times

by Uva@90 » Wed Nov 20, 2013 7:43 pm

kop wrote:Triangles ABC and DEF are similar. What percent of the area of triangle DEF is triangle ABC?

1. Sides AB and DE connect similar angles, and AB is 3 times DE.
2. Side AB = 9

Somebody Please explain me similar triangles properties.
Here to calculate the area we need height?? But how do we get height from the above information?

Hi Kop,
This problem test the below property,

AREA/area = (SIDE)^2/(side)^2, if triangles are similar

I saw lot of similar sum which test above property in the same forum. Worth remembering it.

Regards,
Uva.

Known is a drop Unknown is an Ocean

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Mathsbuddy: Master | Next Rank: 500 Posts; Posts: 447; Joined: Fri Nov 08, 2013 7:25 amFollowed by: 1 member; Thanked: 25 times

by Mathsbuddy » Fri Nov 22, 2013 2:53 am

Area is proportional to length squared

So ratio of Area DEF : Area ABC = 1^2:3^2 = 1:9

1/9 * 100% = 11.1111...%

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