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A ladder 20 feet long is placed against a wall. If the distance on the

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Bunuel
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A ladder 20 feet long is placed against a wall. If the distance on the [#permalink] New post  07 Feb 2022, 09:15
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A ladder 20 feet long is placed against a wall. If the distance on the ground from the wall to the ladder is 12 feet, how many feet up the wall does the ladder reach?

A. 12
B. 15
C. 16
D. 21
E. 24
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Re: A ladder 20 feet long is placed against a wall. If the distance on the [#permalink] New post  07 Feb 2022, 09:37
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This forma a right angled triangle with height of the wall reached as height, horizontal distance of ladder from the ground as base, and ladder as the hypotenuse.
20^2-12^2= 256. √256=16 is the height reached.
Answer option C.

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IanStewart
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Re: A ladder 20 feet long is placed against a wall. If the distance on the [#permalink] New post  07 Feb 2022, 09:51
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We get a right triangle where the 20 foot ladder is the hypotenuse, and the 12 foot distance along the ground is one of the two short sides. That's just 4 times bigger than a 3-4-5 triangle, so the missing vertical side is 16.
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BrentGMATPrepNow
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Re: A ladder 20 feet long is placed against a wall. If the distance on the [#permalink] New post  07 Feb 2022, 09:52
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Bunuel wrote:
A ladder 20 feet long is placed against a wall. If the distance on the ground from the wall to the ladder is 12 feet, how many feet up the wall does the ladder reach?

A. 12
B. 15
C. 16
D. 21
E. 24

Here's what's happening (the ladder is blue)


Since the wall is perpendicular to the ground we can use the Pythagorean theorem to find the value of x
We get: x² + 12² = 20²
Simplify: x² + 144 = 400
This means: x² = 256
So, x = 16
Answer: C


Alternatively, if you recall the Pythagorean triple 3-4-5, you might recognize that the two give sides of our diagram are each 4 times the values in the Pythagorean triple.
In other words 20 = 4(5), and 12 = 4(3)
So, we can conclude that x = 4(4) = 16
Answer: C
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rajatchopra1994
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Re: A ladder 20 feet long is placed against a wall. If the distance on the [#permalink] New post  07 Feb 2022, 09:58
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Explanation:

Ladder reach at inclination:

20^2 - 12^2 = P^2
P^2 = 400 - 144
P^2 = 256
P = 16

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Re: A ladder 20 feet long is placed against a wall. If the distance on the [#permalink]
07 Feb 2022, 09:58
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