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# In the figure below, what is the perimeter of triangle BCD?

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Math Expert
Joined: 02 Sep 2009
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In the figure below, what is the perimeter of triangle BCD?  [#permalink]

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04 Oct 2018, 02:35
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Difficulty:

25% (medium)

Question Stats:

87% (01:31) correct 13% (01:25) wrong based on 41 sessions

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In the figure below, what is the perimeter of triangle BCD?

(A) 4 + 4√3
(B) 12
(C) 12 + 4√3
(D) 8 + 8√3
(E) 16√2

Attachment:

2018-10-04_1334.png [ 18.47 KiB | Viewed 788 times ]

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Re: In the figure below, what is the perimeter of triangle BCD?  [#permalink]

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04 Oct 2018, 06:33
In triangle ABD, by pythagoras theorem - BD=4√3 . And in triangle BCD, with BD as 4√3, by pythgoras theorem- CD=8. So perimeter of traingle BCD= 4+4√3+8= 12+4√3 ans.
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In the figure below, what is the perimeter of triangle BCD?  [#permalink]

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04 Oct 2018, 07:11
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Im not sure if there is a shorter method. I used Pythagorean Theorem twice to solve it.

In Triangle ABD
$$BD^2=AB^2+AD^2$$
$$BD^2=4^2+(4√2)^2=16+32=48$$
$$BD=4√3$$

In Triangle BCD
$$CD^2=BC^2+BD^2$$
$$CD^2=4^2+(4√3)^2$$
$$CD^2=16+16(3)=64$$
CD=8

Perimeter of triangle BCD $$= BC+CD+DB = 4+8+4√3=12+4√3$$
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Re: In the figure below, what is the perimeter of triangle BCD?  [#permalink]

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07 Oct 2018, 19:28
Bunuel wrote:
In the figure below, what is the perimeter of triangle BCD?

(A) 4 + 4√3
(B) 12
(C) 12 + 4√3
(D) 8 + 8√3
(E) 16√2

Attachment:
2018-10-04_1334.png

We can use the Pythagorean theorem to determine the length of side BD:

4^2 + (4√2)^2 = BD^2

16 + 32 = BD^2

48 = BD^2

√48 = BD

Using the Pythagorean theorem we can determine side CD.

4^2 + (√48)^2 = CD^2

16 + 48 = CD^2

64 = CD^2

8 = CD

So the perimeter of triangle BCD is 4 + 8 + √48 = 12 + 4√3

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Re: In the figure below, what is the perimeter of triangle BCD?   [#permalink] 07 Oct 2018, 19:28
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