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In the diagram above, BD = 8, AB = 6, and ED = 5. What is the length

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In the diagram above, BD = 8, AB = 6, and ED = 5. What is the length [#permalink]

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New post 23 Dec 2014, 09:52
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A
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C
D
E

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Tough and Tricky questions: Geometry.



Image
In the diagram above, BD = 8, AB = 6, and ED = 5. What is the length of AE? (Note: Figure not drawn to scale.)

A. 3
B. 4
C. 5
D. 7
E. 10



Kudos for a correct solution.
Attachment:
rectangle_triangle.gif
rectangle_triangle.gif [ 2.54 KiB | Viewed 2972 times ]

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Re: In the diagram above, BD = 8, AB = 6, and ED = 5. What is the length [#permalink]

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New post 23 Dec 2014, 10:23
Given: BD = 8, AB = 6, and ED = 5
Using Pythagoras theorem ==> AD = 10
AE = AD - ED = 5 , Answer C
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Re: In the diagram above, BD = 8, AB = 6, and ED = 5. What is the length [#permalink]

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New post 23 Dec 2014, 21:41
1
Bunuel wrote:

Tough and Tricky questions: Geometry.



Image
In the diagram above, BD = 8, AB = 6, and ED = 5. What is the length of AE? (Note: Figure not drawn to scale.)

A. 3
B. 4
C. 5
D. 7
E. 10



Kudos for a correct solution.
Attachment:
rectangle_triangle.gif



AD^2 = AB^2 + BD^2 = 100 => AD = 10
AE = AD-ED = 5

ANS C
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Re: In the diagram above, BD = 8, AB = 6, and ED = 5. What is the length [#permalink]

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New post 24 Dec 2014, 02:15
2
Answer = C. 5

Attachment:
rectangle_triangle.gif
rectangle_triangle.gif [ 3.46 KiB | Viewed 2528 times ]


Let the required length AE = "a"

\((a+5)^2 = 8^2 + 6^2\)

a+5 = 10

a = 5
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Re: In the diagram above, BD = 8, AB = 6, and ED = 5. What is the length [#permalink]

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New post 24 Dec 2014, 04:50
1
There are two ways to solve this question.
1 We can similar Triangles AEF n CED.
And hence AF=CD.
Now both the triangles are similar. BD/DC=AB/EG=AD/ED results to AD=10. AE=10-5=5.

2. The easiest way just use Pythagorean theorem n U'll get AD=10, AE=10-5=5.

Cheers Guys.
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Re: In the diagram above, BD = 8, AB = 6, and ED = 5. What is the length [#permalink]

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New post 25 Dec 2014, 04:43
1
length of Ad= 10 using pytho. Theorem. Note a pythogerian triple is 3,4,5. This triplet multiplied by 2 is 6,8,10. Hence Ad is 10.

Thus AE=10-5(ED)= 5. Answer is C.
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Re: In the diagram above, BD = 8, AB = 6, and ED = 5. What is the length [#permalink]

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New post 08 Jan 2015, 07:52
Bunuel wrote:

Tough and Tricky questions: Geometry.



Image
In the diagram above, BD = 8, AB = 6, and ED = 5. What is the length of AE? (Note: Figure not drawn to scale.)

A. 3
B. 4
C. 5
D. 7
E. 10



Kudos for a correct solution.
Attachment:
rectangle_triangle.gif


OFFICIAL SOLUTION:

We are given that BD = 8, AB = 6, and ED = 5. Let's break this problem down into a few steps.

1) Since triangle ABD is a right triangle where lengths of the two shorter sides are in the ratio of 4 to 3, the triangle must be a 3-4-5 right triangle (a common right-triangle type).

2) We can find the length of AD.
AB = 3 × 2 = 6
BD = 4 × 2 = 8
Therefore, AD = 5 × 2 = 10.

3) Since AE + ED = AD, AE + 5 = 10

4) AE must equal 5.

The correct answer is choice (C).
_________________

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.


What are GMAT Club Tests?
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Re: In the diagram above, BD = 8, AB = 6, and ED = 5. What is the length [#permalink]

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Re: In the diagram above, BD = 8, AB = 6, and ED = 5. What is the length   [#permalink] 04 Apr 2017, 12:32
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