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# A 20-foot ladder leaning against a vertical wall with the ba

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A 20-foot ladder leaning against a vertical wall with the ba [#permalink]  22 Aug 2018, 09:14
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Question Stats:

75% (01:58) correct 25% (01:11) wrong based on 12 sessions
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A 20-foot ladder leaning against a vertical wall with the base of the ladder 10 feet from the wall is pulled 2 feet farther out from the wall, causing the top of the ladder to drop x feet.

 Quantity A Quantity B x 2

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

Kudos for R.A.E
[Reveal] Spoiler: OA

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Re: A 20-foot ladder leaning against a vertical wall with the ba [#permalink]  25 Aug 2018, 11:00
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Carcass wrote:
Attachment:
triangle.jpg

A 20-foot ladder leaning against a vertical wall with the base of the ladder 10 feet from the wall is pulled 2 feet farther out from the wall, causing the top of the ladder to drop x feet.

 Quantity A Quantity B x 2

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

Kudos for R.A.E

$$20^2 = 12^2 + A^2$$ -> $$A^2 = 400 - 144 = 256$$ -> $$A = \sqrt{256} = 16$$

Similarly,$$20^2 = 10^2 + (16 + x)^2$$ -> $$(16 + x)^2 = 300$$

As 18^2 = 324 > 300 and x must be less than 2

Therefore, we can conclude that Quantity B is greater (Option B)
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Re: A 20-foot ladder leaning against a vertical wall with the ba [#permalink]  28 Aug 2018, 21:34
Use Pythagorean theorum for two lenghts of base(first 10 and then 12) keeping the ladder lengh as 20 to find the difference of the height . the defferece is X .

in first case height will come as 17.32

in second case height will come as 16.00

so X wil be 1.32 < than 2.
Re: A 20-foot ladder leaning against a vertical wall with the ba   [#permalink] 28 Aug 2018, 21:34
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