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# For the triangles above, the perimeter of ABC equals the perimeter of

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Math Expert
Joined: 02 Sep 2009
Posts: 43867
For the triangles above, the perimeter of ABC equals the perimeter of [#permalink]

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29 Aug 2017, 01:25
00:00

Difficulty:

15% (low)

Question Stats:

97% (00:23) correct 3% (00:00) wrong based on 47 sessions

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For the triangles above, the perimeter of ABC equals the perimeter of DEF. If ∆ ABC is equilateral, what is the length of side AB?

(A) 4
(B) 5
(C) 7
(D) 9
(E) 15

[Reveal] Spoiler:
Attachment:

2017-08-29_1322.png [ 8.62 KiB | Viewed 623 times ]
[Reveal] Spoiler: OA

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Re: For the triangles above, the perimeter of ABC equals the perimeter of [#permalink]

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29 Aug 2017, 01:33
Bunuel wrote:

For the triangles above, the perimeter of ABC equals the perimeter of DEF. If ∆ ABC is equilateral, what is the length of side AB?

(A) 4
(B) 5
(C) 7
(D) 9
(E) 15

[Reveal] Spoiler:
Attachment:
2017-08-29_1322.png

Perimeter of ∆ DEF $$= 4 + 8 + 9 = 21$$

Perimeter of ∆ DEF $$=$$ Perimeter of ∆ ABC $$= 21$$

∆ ABC is equilateral. Therefore all the sides are equal.

Therefore AB $$= \frac{21}{3} = 7$$

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Posts: 2014
Re: For the triangles above, the perimeter of ABC equals the perimeter of [#permalink]

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01 Sep 2017, 11:10
Bunuel wrote:

For the triangles above, the perimeter of ABC equals the perimeter of DEF. If ∆ ABC is equilateral, what is the length of side AB?

(A) 4
(B) 5
(C) 7
(D) 9
(E) 15

Triangle DEF has a perimeter of 4 + 8 + 9 = 21. Since triangle ABC is equilateral (with all sides equal) and has the same perimeter as triangle DEF, we can create the following equation to determine n where n = a side of triangle ABC:

3n = 21

n = 7

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Re: For the triangles above, the perimeter of ABC equals the perimeter of [#permalink]

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07 Sep 2017, 12:49
Perimeter of triangle DEF = 4+8+9 = 21

Now the perimeter of ABC equals the perimeter of DEF. Also , triangle ABC is equilateral triangle , means each side equal.

Thus AB =BC= AC = 21/3 = 7

Correct option : C
Re: For the triangles above, the perimeter of ABC equals the perimeter of   [#permalink] 07 Sep 2017, 12:49
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