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# An equilateral Triangle has a square inscribed in it, side

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An equilateral Triangle has a square inscribed in it, side [#permalink]  02 Oct 2012, 22:51
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Question Stats:

87% (01:29) correct 12% (03:53) wrong based on 8 sessions
An equilateral Triangle has a square inscribed in it, side of square =12 inch. What is the perimeter of the triangle?

A. 36 inch
B. 36 root3 inch
C. 36 root3 inch + 24 inch
D. 72 inch
E. 24 root3 + 36 inch

Last edited by Bunuel on 03 Oct 2012, 02:57, edited 1 time in total.
Renamed the topic and edited the question.
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Re: An equilateral Triangle has a sqaure inscribed in it, side o [#permalink]  03 Oct 2012, 00:36
1
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An equilateral Triangle has a sqaure inscribed in it, side of sqaure =12 inch.
What is the perimeter of the triangle?
A. 36 inch
B.36 root3 inch
C.36 root3 inch + 24 inch
D.72 inch
E.24 root3 + 36 inch

Figure attached

ABC is equilateral traingle and DEFG is the square inscribed in it.
Since DE || FG so DE || BC so, <ADE = <B = 60 and <AED = <C = 60
So, Traingle ADE is equialteral. Similarly we can prove that Traingle DBG and Triangle ECF are equialteral.
So, AD = DE = 12inch

PErimeter of the traingle = 3*AB = 3*24= 72inch.

Hope it helps!
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Re: An equilateral Triangle has a sqaure inscribed in it, side o [#permalink]  16 Oct 2012, 03:12
3
KUDOS
nktdotgupta wrote:
An equilateral Triangle has a sqaure inscribed in it, side of sqaure =12 inch.
What is the perimeter of the triangle?
A. 36 inch
B.36 root3 inch
C.36 root3 inch + 24 inch
D.72 inch
E.24 root3 + 36 inch

Figure attached

ABC is equilateral traingle and DEFG is the square inscribed in it.
Since DE || FG so DE || BC so, <ADE = <B = 60 and <AED = <C = 60
So, Traingle ADE is equialteral. Similarly we can prove that Traingle DBG and Triangle ECF are equialteral.
So, AD = DE = 12inch

PErimeter of the traingle = 3*AB = 3*24= 72inch.

Hope it helps!

Triangle ADE is an equilateral triangle, but the other two triangles are not(however both are similar Tirangles).

Solving for BDG:

angle DBG=60(as per Q)
angle BG=90
hence, angle BDG=30.
the raito of sides for a 30,60,90 triangle >> 1:root3:2( refer to Bunuel's post math-triangles-87197.html)
since DG=12
BG = 12/root3
hence : using P&T :>> DB = 24*root3

Same applies for the triangle EFC

therefore, Perimeter =DA+DB+BG+GF+FC+CE+EA
=12+24/root3+12/root3+12+12/root3+24/root3 +12
=36+72/root3
=36+(24*root3*root3)/root3
=36+24*root3

hope the u dont mind the poor formatting
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Re: An equilateral Triangle has a sqaure inscribed in it, side o [#permalink]  18 May 2013, 11:49
Maverick04308 wrote:
nktdotgupta wrote:
An equilateral Triangle has a sqaure inscribed in it, side of sqaure =12 inch.
What is the perimeter of the triangle?
A. 36 inch
B.36 root3 inch
C.36 root3 inch + 24 inch
D.72 inch
E.24 root3 + 36 inch

Figure attached

ABC is equilateral traingle and DEFG is the square inscribed in it.
Since DE || FG so DE || BC so, <ADE = <B = 60 and <AED = <C = 60
So, Traingle ADE is equialteral. Similarly we can prove that Traingle DBG and Triangle ECF are equialteral.
So, AD = DE = 12inch

PErimeter of the traingle = 3*AB = 3*24= 72inch.

Hope it helps!

Triangle ADE is an equilateral triangle, but the other two triangles are not(however both are similar Tirangles).

Solving for BDG:

angle DBG=60(as per Q)
angle BG=90
hence, angle BDG=30.
the raito of sides for a 30,60,90 triangle >> 1:root3:2( refer to Bunuel's post math-triangles-87197.html)
since DG=12
BG = 12/root3
hence : using P&T :>> DB = 24*root3

Same applies for the triangle EFC

therefore, Perimeter =DA+DB+BG+GF+FC+CE+EA
=12+24/root3+12/root3+12+12/root3+24/root3 +12
=36+72/root3
=36+(24*root3*root3)/root3
=36+24*root3

hope the u dont mind the poor formatting

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Re: An equilateral Triangle has a sqaure inscribed in it, side o [#permalink]  18 May 2013, 12:04
Hi,

Ans is E. You are assuming AB=2AD, which is wrong.

DB = 8sqrt3
so AB = 8sqrt3 + 12
so perimeter = 24sqrt3 + 36

nktdotgupta wrote:
An equilateral Triangle has a sqaure inscribed in it, side of sqaure =12 inch.
What is the perimeter of the triangle?
A. 36 inch
B.36 root3 inch
C.36 root3 inch + 24 inch
D.72 inch
E.24 root3 + 36 inch

Figure attached

ABC is equilateral traingle and DEFG is the square inscribed in it.
Since DE || FG so DE || BC so, <ADE = <B = 60 and <AED = <C = 60
So, Traingle ADE is equialteral. Similarly we can prove that Traingle DBG and Triangle ECF are equialteral.
So, AD = DE = 12inch

PErimeter of the traingle = 3*AB = 3*24= 72inch.

Hope it helps!
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Posts: 619
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Re: An equilateral Triangle has a sqaure inscribed in it, side o [#permalink]  18 May 2013, 21:43
Expert's post
nktdotgupta wrote:

So, Traingle ADE is equialteral. Similarly we can prove that Traingle DBG and Triangle ECF are equialteral.

I am afraid but this part is not correct.
Triangles DBG and ECF are NOT equilateral.
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Re: An equilateral Triangle has a sqaure inscribed in it, side o   [#permalink] 18 May 2013, 21:43
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