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

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Math Expert
Joined: 02 Sep 2009
Posts: 52108
In the diagram above, BD = 8, AB = 6, and ED = 5. What is the length  [#permalink]

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23 Dec 2014, 08:52
1
1
00:00

Difficulty:

5% (low)

Question Stats:

88% (00:59) correct 12% (01:29) wrong based on 124 sessions

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Tough and Tricky questions: Geometry.

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 [ 2.54 KiB | Viewed 3614 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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23 Dec 2014, 09:23
1
Given: BD = 8, AB = 6, and ED = 5
Using Pythagoras theorem ==> AD = 10
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GMAT 1: 700 Q49 V35
Re: In the diagram above, BD = 8, AB = 6, and ED = 5. What is the length  [#permalink]

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23 Dec 2014, 20:41
1
Bunuel wrote:

Tough and Tricky questions: Geometry.

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

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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24 Dec 2014, 01:15
2

Attachment:

rectangle_triangle.gif [ 3.46 KiB | Viewed 3104 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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24 Dec 2014, 03:50
1
There are two ways to solve this question.
1 We can similar Triangles AEF n CED.
And hence AF=CD.

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

Cheers Guys.
Please Press Kundu if the Explanation helps You.
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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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25 Dec 2014, 03:43
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.
Math Expert
Joined: 02 Sep 2009
Posts: 52108
Re: In the diagram above, BD = 8, AB = 6, and ED = 5. What is the length  [#permalink]

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08 Jan 2015, 06:52
Bunuel wrote:

Tough and Tricky questions: Geometry.

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).
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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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16 Dec 2018, 15:37
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Re: In the diagram above, BD = 8, AB = 6, and ED = 5. What is the length &nbs [#permalink] 16 Dec 2018, 15:37
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