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# Triangles

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Manager
Joined: 30 Dec 2008
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12 Jan 2009, 19:16
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

2 Triangles with the same angles (same x, y, z degrees for each side).
area of triangle B is twice the area of triangle A.
if s is the base of triangle A, what is the base of triangle B in terms of s?
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Manager
Status: Stanford GSB
Joined: 02 Jun 2008
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13 Jan 2009, 12:28
Triangles with the same angles (same x, y, z degrees for each side).
area of triangle B is twice the area of triangle A.
if s is the base of triangle A, what is the base of triangle B in terms of s?

To test a simple case, lets assume both the triangles are right angled ones.
Height Base Area
Triangle A 1 2 ½*1*2= 1
Triangle B Root 2 2* root 2 2

Hence is s is the base of triange A, the base of B will be (root 2*s)

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Manager
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13 Jan 2009, 14:32
But can you clarify the explanation a little bit.
are you using 90-60-30? what's the approach?

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Manager
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13 Jan 2009, 14:52
Actually there was a table in my answer which has vanished after posting.
I have taken the simple most case to calculate the chage.
lets assume both the triangles are right angled ones.
Height Base Area
In Triangle A ,
base = 2,height =1 hence the area= 1/2* base* height= 1

In Traingle B,
Base = ? Height =? Area =2 ( 2 times than A)

Now in B, Area=1/2* base* height= 2
or, base*height=4

As both triangle A and B are with same angles the ratio of their sides would be same.
hence base=2*height

by putting this in earler equation,
2* height square= 4
height square= 2
height= root 2
base = 2* root 2

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Manager
Joined: 12 Aug 2008
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13 Jan 2009, 15:45
Correct me if am wrong, but aren't the two triangles similar? If so:

Area of A = x
Base of A = s
Area of B = 2x
Base of B = y

Given the triangles are similar:

Area of A / Area of B = (Base of A)^2 / (Base of B) ^2

x/2x= (s^2)/(y^2)
y^2= 2*(s^2)
y = s*sqr2

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Manager
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13 Jan 2009, 18:10
both of you arrived at the right answer.
Thanks for clarifying sandip.

sid3699, is that a formula for similar triangles? ---? ratio of area = ratio of base squared?
what other formulas can we applied if we know it's a similar triangle?

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Manager
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14 Jan 2009, 09:53
cul3s wrote:
both of you arrived at the right answer.
Thanks for clarifying sandip.

sid3699, is that a formula for similar triangles? ---? ratio of area = ratio of base squared?
what other formulas can we applied if we know it's a similar triangle?

Its not just the base. One can use any corresponding pair in the above formula.

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SVP
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16 Jan 2009, 14:28
cul3s wrote:
2 Triangles with the same angles (same x, y, z degrees for each side).
area of triangle B is twice the area of triangle A.
if s is the base of triangle A, what is the base of triangle B in terms of s?

7-t74793
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Re: Triangles   [#permalink] 16 Jan 2009, 14:28
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