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In the diagram below, AB = 3, AD = 4, and BC = 12. What is the perimet

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Bunuel
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In the diagram below, AB = 3, AD = 4, and BC = 12. What is the perimet [#permalink] New post   23 Dec 2020, 09:30
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In the diagram below, AB = 3, AD = 4, and BC = 12. What is the perimeter of the quadrilateral?

(A) 32
(B) 30
(C) 28
(D) 26
(E) 24


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bobnil
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Re: In the diagram below, AB = 3, AD = 4, and BC = 12. What is the perimet [#permalink] New post   23 Dec 2020, 09:46
For, triangle ABD, BD =5 (Considering pythegorian triplets 3-4-5).
For triangle BCD, DC= sqrt(25+144)
= 13.
So,reqd perimeter = 3+4+13+12 =32
Ans A

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In the diagram below, AB = 3, AD = 4, and BC = 12. What is the perimet [#permalink] New post   23 Dec 2020, 09:49
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3 , 4 , 5

5 , 12 , 13

final ans = 3+4+12+13 = 32 .... A
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Re: In the diagram below, AB = 3, AD = 4, and BC = 12. What is the perimet [#permalink] New post   23 Dec 2020, 09:55
Given:
1. ∆ABD & ∆BDC are Right Angle Triangles.
2. AB=3, AD=4, BC=12

To find: Perimeter of ABCD.

Solving: ∆ABD
By using Pythagoras theorem we will get side BD.
BD^2 = AB^2 + AD^2 =25
BD = 5

Solving: ∆BDC
By using Pythagoras theorem we will get side CD.
CD^2 = BD^2 + BC^2 = 169
CD = 13

Perimeter of ABCD: AB+BC+CD+DA = 3+12+13+4= 32

Answer: A

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Re: In the diagram below, AB = 3, AD = 4, and BC = 12. What is the perimet [#permalink] New post   23 Dec 2020, 10:43
Bunuel wrote:

In the diagram below, AB = 3, AD = 4, and BC = 12. What is the perimeter of the quadrilateral?

(A) 32
(B) 30
(C) 28
(D) 26
(E) 24


Show Spoiler
Attachment:
2020-12-21_17-17-58.png


IMO A

Triangle ADB is an Right Angle Triangle
3^2 + 4^2 = DB^2
5 = DB

Triangle DBC Right Angle
DB^2 + BC^2 = DC^2
13 = DC


Perimeter = Sum of all sides
DB +BC + CD + DA = 4+3+12+13 = 32
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Re: In the diagram below, AB = 3, AD = 4, and BC = 12. What is the perimet [#permalink] New post   23 Dec 2020, 10:50
ShankSouljaBoi wrote:
3 , 4 , 5

5 , 12 , 13

final ans = 3+4+12+13 = 32 .... A

Using Pythagorean triples form....

Short and cute way to solve this problem in seconds, Kudos added :ok :ok :ok :student_man: :student_man: :student_man:
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Re: In the diagram below, AB = 3, AD = 4, and BC = 12. What is the perimet [#permalink]
23 Dec 2020, 10:50
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