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

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Math Expert
Joined: 02 Sep 2009
Posts: 52231
In the figure above, triangle CDE is an equilateral triangle with side  [#permalink]

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07 Sep 2015, 22:02
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Difficulty:

25% (medium)

Question Stats:

84% (02:05) correct 16% (02:50) wrong based on 124 sessions

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

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08 Sep 2015, 00:41
1
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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08 Sep 2015, 10:14
1
[quote="Bunuel"]
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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08 Sep 2015, 12:18
1
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;
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Re: In the figure above, triangle CDE is an equilateral triangle with side  [#permalink]

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11 Sep 2015, 11:01
1
Bunuel wrote:

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.

Attachment:
triangles.gif

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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11 Sep 2015, 11:15
1
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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14 Sep 2015, 05:40
Bunuel wrote:

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.

Attachment:
The attachment triangles.gif is no longer available

GROCKIT OFFICIAL SOLUTION:

The question tells us this much:

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:

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.

Attachment:

triangles3.gif [ 4.36 KiB | Viewed 2541 times ]

Attachment:

triangles2.gif [ 4.31 KiB | Viewed 2553 times ]

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

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