Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 60646

The length of a ladder is exactly equal to the height of the wall. If
[#permalink]
Show Tags
24 Oct 2019, 22:28
Question Stats:
74% (01:58) correct 26% (02:42) wrong based on 53 sessions
HideShow timer Statistics
Competition Mode Question 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
Official Answer and Stats are available only to registered users. Register/ Login.
_________________



VP
Joined: 20 Jul 2017
Posts: 1262
Location: India
Concentration: Entrepreneurship, Marketing
WE: Education (Education)

Re: The length of a ladder is exactly equal to the height of the wall. If
[#permalink]
Show Tags
24 Oct 2019, 22:43
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 rightangled 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



Senior Manager
Joined: 01 Mar 2019
Posts: 404
Location: India
Concentration: Strategy, Social Entrepreneurship
GPA: 4

Re: The length of a ladder is exactly equal to the height of the wall. If
[#permalink]
Show Tags
24 Oct 2019, 22:49
OA:B
Attachments
IMG_20191025_111546444.jpg [ 2.48 MiB  Viewed 816 times ]



VP
Joined: 19 Oct 2018
Posts: 1295
Location: India

Re: The length of a ladder is exactly equal to the height of the wall. If
[#permalink]
Show Tags
25 Oct 2019, 00:04
length of Ladder, AC= x Length of wall, CE= x CB=x2 Triangle ABC is a right angle triangle Hence, \(AB^2+BC^2=AC^2\) {pythagoras theorem} \(10^2+(x2)^2=x^2\) x= 26 ft
Attachments
Untitled.png [ 5.24 KiB  Viewed 763 times ]



Director
Joined: 07 Mar 2019
Posts: 597
Location: India
WE: Sales (Energy and Utilities)

Re: The length of a ladder is exactly equal to the height of the wall. If
[#permalink]
Show Tags
25 Oct 2019, 00:37
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 nonparallel sides of length '10' and 'x'. Refer diagram below. Attachment: File comment: Ladder Wall
Ladder Wall.png [ 13.44 KiB  Viewed 643 times ]
In right angled triangle ADE, x^2 = 10^2 + (x  2)^2 Solving the equation gives x = 26 Answer B.
_________________
Ephemeral Epiphany..!
GMATPREP1 590(Q48,V23) March 6, 2019 GMATPREP2 610(Q44,V29) June 10, 2019 GMATPREPSoft1 680(Q48,V35) June 26, 2019



GMAT Club Legend
Joined: 18 Aug 2017
Posts: 5732
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)

Re: The length of a ladder is exactly equal to the height of the wall. If
[#permalink]
Show Tags
25 Oct 2019, 03:32
from given info we can say height of ladder =x x^2= (x2)^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



Intern
Joined: 27 Mar 2019
Posts: 1

Re: The length of a ladder is exactly equal to the height of the wall. If
[#permalink]
Show Tags
25 Oct 2019, 03:36
Let: height of the wall = h; length of ladder= l Given, h=l Since ladder is placed on top of the stool, the relative height till it touches the wall= (h2)ft Since the ladder is placed 10ft away from the wall, the horizontal distance= 10ft Applying Pythagoras Theorem, (h2)^2 + 10^2 = h^2 Thus, h^2  4h +4 + 100 = h^2 Thus, h= 104/4 Thus, h= 26 ______ [ Option B ]
_________________



VP
Joined: 24 Nov 2016
Posts: 1110
Location: United States

Re: The length of a ladder is exactly equal to the height of the wall. If
[#permalink]
Show Tags
25 Oct 2019, 03:54
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: hypotenuse x (ladder) base 10 (floor) height x2 (wall minus the stool) \(x^2=(x2)^2+10^2…x^2=x^2+44x+100…4(x1)=100…x=25+1=26\) Answer (B)



Director
Joined: 18 May 2019
Posts: 665

Re: The length of a ladder is exactly equal to the height of the wall. If
[#permalink]
Show Tags
25 Oct 2019, 05:36
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 (h2). We are to determine the height of the wall, h. From the calculations in the figure below, h=26ft The answer is therefore B.Posted from my mobile device
Attachments
image.jpg [ 1.74 MiB  Viewed 672 times ]



Senior Manager
Joined: 25 Jul 2018
Posts: 483

Re: The length of a ladder is exactly equal to the height of the wall. If
[#permalink]
Show Tags
25 Oct 2019, 14:14
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
The answer is B
Posted from my mobile device



Manager
Joined: 17 Jan 2019
Posts: 150

Re: The length of a ladder is exactly equal to the height of the wall. If
[#permalink]
Show Tags
27 Oct 2019, 20:38
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
(x2)^2+10^2=x^2 x^24x4+100=x^2 4x4=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






