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# The length of a ladder is exactly equal to the height of the wall. If

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Math Expert
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The length of a ladder is exactly equal to the height of the wall. If  [#permalink]

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24 Oct 2019, 22:28
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45% (medium)

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75% (01:55) correct 25% (02:46) wrong based on 51 sessions

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The length of a ladder is exactly equal to the height of the wall. If a ladder is placed on a 2 ft stool, placed 10 ft away from the wall, then the top of the ladder just reaches the top of the wall.Find the height of the wall.

(A) 25
(B) 26
(C) 27
(D) 28
(E) 29

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Re: The length of a ladder is exactly equal to the height of the wall. If  [#permalink]

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24 Oct 2019, 22:43
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Let the height of the wall = h = length of the ladder

When it is placed on a stool of 2 ft height, base of the ladder is 10 ft away from the wall.
So a right-angled triangle is formed with hypotenuse = h, base = 10 and height = (h - 2)

--> $$h^2 = (h - 2)^2 + 10^2$$
--> $$h^2 = h^2 - 4h + 4 + 100$$
--> $$4h = 104$$
--> $$h = 26$$

Height of the wall = h = 26

IMO Option B
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Re: The length of a ladder is exactly equal to the height of the wall. If  [#permalink]

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24 Oct 2019, 22:49
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OA:B
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Re: The length of a ladder is exactly equal to the height of the wall. If  [#permalink]

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25 Oct 2019, 00:04
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1
Length of wall, CE= x

CB=x-2

Triangle ABC is a right angle triangle

Hence, $$AB^2+BC^2=AC^2$$ {pythagoras theorem}

$$10^2+(x-2)^2=x^2$$

x= 26 ft
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Re: The length of a ladder is exactly equal to the height of the wall. If  [#permalink]

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25 Oct 2019, 00:37
1
The length of a ladder is exactly equal to the height of the wall. If a ladder is placed on a 2 ft stool, placed 10 ft away from the wall, then the top of the ladder just reaches the top of the wall.Find the height of the wall.

(A) 25
(B) 26
(C) 27
(D) 28
(E) 29

Let 'x' be the height of ladder and wall. As described in question the ladder and wall would form a trapezium with parallel sides of length 'x' and '2' and non-parallel sides of length '10' and 'x'. Refer diagram below.

Attachment:

Ladder Wall.png [ 13.44 KiB | Viewed 604 times ]

In right angled triangle ADE, x^2 = 10^2 + (x - 2)^2

Solving the equation gives x = 26

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Re: The length of a ladder is exactly equal to the height of the wall. If  [#permalink]

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25 Oct 2019, 03:32
1
from given info
we can say
x^2= (x-2)^2+10^2
solve for x = 24 + 2 ; 26
IMO B

The length of a ladder is exactly equal to the height of the wall. If a ladder is placed on a 2 ft stool, placed 10 ft away from the wall, then the top of the ladder just reaches the top of the wall.Find the height of the wall.

(A) 25
(B) 26
(C) 27
(D) 28
(E) 29
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Joined: 27 Mar 2019
Posts: 1
Re: The length of a ladder is exactly equal to the height of the wall. If  [#permalink]

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25 Oct 2019, 03:36
1
Let:
height of the wall = h;

Given, h=l
Since ladder is placed on top of the stool, the relative height till it touches the wall= (h-2)ft
Since the ladder is placed 10ft away from the wall, the horizontal distance= 10ft

Applying Pythagoras Theorem, (h-2)^2 + 10^2 = h^2
Thus, h^2 - 4h +4 + 100 = h^2
Thus, h= 104/4
Thus, h= 26 ______ [Option B ]
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Re: The length of a ladder is exactly equal to the height of the wall. If  [#permalink]

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25 Oct 2019, 03:54
1
Quote:
The length of a ladder is exactly equal to the height of the wall. If a ladder is placed on a 2 ft stool, placed 10 ft away from the wall, then the top of the ladder just reaches the top of the wall.Find the height of the wall.

(A) 25
(B) 26
(C) 27
(D) 28
(E) 29

imagine a triangle:
base 10 (floor)
height x-2 (wall minus the stool)

$$x^2=(x-2)^2+10^2…x^2=x^2+4-4x+100…4(x-1)=100…x=25+1=26$$

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Re: The length of a ladder is exactly equal to the height of the wall. If  [#permalink]

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25 Oct 2019, 05:36
1
height of wall=height of ladder, h
We are given that the ladder is placed on a stool which is 2ft tall, and the stool is 10ft away from the wall. The height of the wall referenced to the stool is now (h-2).
We are to determine the height of the wall, h.

From the calculations in the figure below, h=26ft

Posted from my mobile device
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Re: The length of a ladder is exactly equal to the height of the wall. If  [#permalink]

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25 Oct 2019, 14:14
1
The length of the ladder = the length of the wall. —let x be the length of them

—> if ladder is placed on a 2 ft long stool, placed 10 ft away from the wall and leaned against the wall, then the top of ladder reaches the top of the wall.
—> the right—angled triangle can be drawn
—> $$x^{2}$$= $$10^{2}+ (x—2)^{2}$$

$$x^{2}= 100+ x^{2}—4*x+ 4$$
4*x= 104
x =26

Posted from my mobile device
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Re: The length of a ladder is exactly equal to the height of the wall. If  [#permalink]

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27 Oct 2019, 20:38
1
x is the height of the wall
x is the length of the ladder
10 is the distance of the ground between the wall and the ladder

(x-2)^2+10^2=x^2
x^2-4x-4+100=x^2
4x-4=100
4x=104
x=26

Therefore, B
Re: The length of a ladder is exactly equal to the height of the wall. If   [#permalink] 27 Oct 2019, 20:38
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