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# What is the length of AD in the figure above?

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Math Expert
Joined: 02 Sep 2009
Posts: 58396

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18 Jan 2019, 00:18
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Difficulty:

15% (low)

Question Stats:

85% (00:58) correct 15% (02:01) wrong based on 31 sessions

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What is the length of AD in the figure above?

A 3√5
B 3√3
C 8
D 8√3
E 9√2

Attachment:

2019-01-18_1116.png [ 8.1 KiB | Viewed 617 times ]

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Re: What is the length of AD in the figure above?  [#permalink]

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18 Jan 2019, 06:48
Bunuel wrote:

What is the length of AD in the figure above?

A 3√5
B 3√3
C 8
D 8√3
E 9√2

Attachment:
2019-01-18_1116.png

BC = 8
so side of base = 8-5 = 3
apply phythogerous
6^2 +3^2 = sqrt 45
IMO A 3√5
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Re: What is the length of AD in the figure above?  [#permalink]

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19 Jan 2019, 00:49
Pythagorean triples to know are 3-4-5 and 5-12-13
Recognise that 6-8-10 is double 3-4-5

The bottom edge of the large triangle is 8.
8-5=3

$$3^2+6^2=h^2$$
9+36=$$h^2$$
h=√45
h=√(9·5)
h=√9·√5
h=3√5
Re: What is the length of AD in the figure above?   [#permalink] 19 Jan 2019, 00:49
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