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In the figure above, triangle CDE is an equilateral triangle with side

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In the figure above, triangle CDE is an equilateral triangle with side [#permalink]

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In the figure above, triangle CDE is an equilateral triangle with side length 3, AF = 10, EF = 6, and AB = DE. What is the perimeter of the figure?

(A) 45
(B) 36
(C) 29
(D) 24
(E) 16

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[Reveal] Spoiler:
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[Reveal] Spoiler: OA

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Re: In the figure above, triangle CDE is an equilateral triangle with side [#permalink]

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New post 08 Sep 2015, 00:41
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Using pythagoras theorem,

In triangle AEF
AE=8 and hence AC=5

Again in Triangle ABC,
BC=4

Hence perimeter = 10(AF)+6(EF)+3(DE)+3(DC)+4(BC)+3(AB)=29

Option C.

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Re: In the figure above, triangle CDE is an equilateral triangle with side [#permalink]

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[quote="Bunuel"]Image
AB=3
CD=3
DE=3
AF=10
EF=6

Triangle ABC is a 3-4-5 triangle, so BC=4
3+4+3+3+6+10 = 29

(C) 29
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Re: In the figure above, triangle CDE is an equilateral triangle with side [#permalink]

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New post 08 Sep 2015, 12:18
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In ▲ AFE, rt. angled at E, AF = 10, EF = 6, → AE² = 10² + 6² → AE = 8;
In ▲ DCE, DC = DE = CE = 3, → AC = AE-CE = 8-3 = 5;
In ▲ ABC, AB = DE =3, AC = 5, BC² = AC² - AB² → BC = 4;
Perimeter of the figure = AB+BC+DC+DE+EF+AF = 3+4+3+3+6+10 = 29;
Answer: C
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Re: In the figure above, triangle CDE is an equilateral triangle with side [#permalink]

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Bunuel wrote:
Image
In the figure above, triangle CDE is an equilateral triangle with side length 3, AF = 10, EF = 6, and AB = DE. What is the perimeter of the figure?

(A) 45
(B) 36
(C) 29
(D) 24
(E) 16

Kudos for a correct solution.

[Reveal] Spoiler:
Attachment:
triangles.gif


Correct answer is C

By using Pythagoras theorem,

In triangle AEF,
AE=8 and hence AC=5

In Triangle ABC,
BC=4

Hence perimeter = 10(AF)+6(EF)+3(DE)+3(DC)+4(BC)+3(AB)

=29
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Re: In the figure above, triangle CDE is an equilateral triangle with side [#permalink]

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New post 11 Sep 2015, 11:15
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perimeter of the figure ABCDEF = AB+BC+CD+DE+EF+AF

everything given except BC.


Calculate AC from the triangle AEF

AC +CE=8 , AC =8-3=5

Now calculate BC

BC = [(AC) 2- (AB)2]^1/2= (25-9)^1/2=4

now perimeter is: AB+BC+CD+DE+EF+AF =3+4+3+3+6+10=29

Ans is C

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In the figure above, triangle CDE is an equilateral triangle with side [#permalink]

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New post 14 Sep 2015, 05:40
Bunuel wrote:
Image
In the figure above, triangle CDE is an equilateral triangle with side length 3, AF = 10, EF = 6, and AB = DE. What is the perimeter of the figure?

(A) 45
(B) 36
(C) 29
(D) 24
(E) 16

Kudos for a correct solution.

[Reveal] Spoiler:
Attachment:
The attachment triangles.gif is no longer available


GROCKIT OFFICIAL SOLUTION:

The question tells us this much:

Image

From here, we can deduce that:

1. Triangle AEF is a 3:4:5 triangle, with side lengths 6:8:10, respectively.

2. Since AE is 8 and CE is 3, that makes AC = 5.

3. Since AC = 5, triangle ABC is also a 3:4:5 triangle, and BC = 4

We can then have:

Image

10+6+4+(3*3) = 29. Answer choice (A) 45 is the sum of the perimeters of each of the triangles, rather than the perimeter of the figure.

[Reveal] Spoiler:
Attachment:
triangles3.gif
triangles3.gif [ 4.36 KiB | Viewed 1853 times ]

Attachment:
triangles2.gif
triangles2.gif [ 4.31 KiB | Viewed 1866 times ]

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: In the figure above, triangle CDE is an equilateral triangle with side [#permalink]

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Re: In the figure above, triangle CDE is an equilateral triangle with side   [#permalink] 22 Apr 2017, 03:27
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