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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:

74% (01:27) correct 25% (02:24) wrong based on 59 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.

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[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
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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.
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Re: A 20-foot ladder leaning against a vertical wall with the ba [#permalink]  06 Sep 2020, 15:39
So does that mean after the ladder pulled away from the wall slop remains as 20?
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Re: A 20-foot ladder leaning against a vertical wall with the ba [#permalink]  07 Sep 2020, 12:29
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Anjani wrote:
So does that mean after the ladder pulled away from the wall slop remains as 20?

The 20 doesn't represent the slope of the ladder; it represents the length of the ladder.
The ladder is 20 feet long.
When the base of the ladder is 10 feet from the wall, the top of the ladder is a certain height.

When we move the base of the ladder so that it is now 12 feet from the wall, the top of the ladder drops x feet.

The question wants you to find the value of x
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Re: A 20-foot ladder leaning against a vertical wall with the ba   [#permalink] 07 Sep 2020, 12:29
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