Latest TCS Aptitude Question SOLUTION: if a ladder is 100m long, and distance b/w bottom of ladder and wall is 60. top side of bottom and wall is joint. what is the maximum size of cube that place b/t them.

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(#M40012686) TCS Numerical Ability question Keep an EYE

if a ladder is 100m long, and distance b/w bottom of ladder and wall is 60. top side of bottom and wall is joint.
what is the maximum size of cube that place b/t them.

Asked In TCS Vikas kumar gupta (11 years ago)

Unsolved Read Solution (28)

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Read Solution (28) :

Sahil Motwani  (11 years ago)

The answer is 35. it is a simple pythagorus thm problem.let the edge of cube be x. now make a square between a right angled triangle of base 60 hypotnuse 100 and height is calculated to be 80. now due to square two right triangles are formed. so the hypo of 1st tri. + hypo. of 2nd tri. should be equal to 100.
therefore (60-x)^2 +x^2 + x^2 + (80-x)^2 = 100.

Is this solution Helpfull? Yes (37) | No (14)  

Aditya Singh Chauhan  (11 years ago)

35.....
using trigonometry we have
(80/60)=tan(y)....1
(x/60-x)=tan(y)....2
solve it... u will have 35

Is this solution Helpfull? Yes (16) | No (1)  

prateek lokhande  (11 years ago)

i think 30

Is this solution Helpfull? Yes (11) | No (8)  

hemanth  (8 years ago)

let x be side of cube
80/x=60/60-x
ans: x=34.28

Is this solution Helpfull? Yes (9) | No (2)  

Vikrant Varshney  (11 years ago)

how?
i m not getting que. exactly.

Is this solution Helpfull? Yes (6) | No (5)  

RAVINDRA KUMAR YADAV  (11 years ago)

sorry friends there was a mistake in my previous answer..exact answer is 34
since line passing through (60,0) and (0,80)is 4x+3y-240=0
put x=y=35, we get 5>0.
so point (35,35)lies outside the triangle, but 34 lies inside the triangle
so size=34

Is this solution Helpfull? Yes (6) | No   

Pallavi Barjatiya  (11 years ago)

yes.. i too nt abl to get. . who is givin ans.
please. .xplain qs. n ans both?

Is this solution Helpfull? Yes (5) | No (9)  

RAVINDRA KUMAR YADAV  (11 years ago)

APPLYING pythagorus theorem-let side of square be x unit ,then the base and height of triangle are devided in 60-x and 80-x .
(60-x)^2+x^2+(80-x)^2+x^2=100^2=4(x^2)-280*x=0
4x(x-70)=0
Xmax=70 but it goes outside the triangle so Xmax=Xmax/2=35

Is this solution Helpfull? Yes (5) | No (2)  

purnima digra  (8 years ago)

hypotune=100
base=60
so length=80
max side of cube that can fit into it will be HCF OF 100 60 80
that is 20
so diagonal of that cube will be 20*sqrt3=34.65

Is this solution Helpfull? Yes (3) | No   

venkatrao  (11 years ago)

Exactly 30

Is this solution Helpfull? Yes (2) | No (8)  

kulkarni sneha  (11 years ago)

plz give solution... with details

Is this solution Helpfull? Yes (2) | No (2)  

MIR FIROJ ALI  (11 years ago)

it should be square with side 66/2=33

so area of cube is 33^3=35937

Is this solution Helpfull? Yes (2) | No (6)  

Preeti kureel  (11 years ago)

by pythagorus height of triangle formed=80
area of triangle=1/2* base*height
=1/2*60*80
=2400
to fit the square area must be perfect square
so 2400-96=2304(which is a perfect square)
area of sq.=2304
side=48
maximum size=4*48=192

Is this solution Helpfull? Yes (2) | No (11)  

adarsh  (8 years ago)

when we are insert a cube into triangle it divides the triangle in to two sub triangles.
so area old triangle= area of square + area of sub triangle1 + area of sub triangle2.
1/2(60*80)=1/2((60-x)*x)+1/2((80-x)*x)+x^2..
if we solve this we will get 34.26

Is this solution Helpfull? Yes (2) | No   

rahul  (11 years ago)

i m not able to get the answer so plz explain

Is this solution Helpfull? Yes | No   

dhyanendra mani tripathi  (11 years ago)

dra a right angled triangle and draw a square in it with side x. then at the base u will get two parts one is x and other is 60-x. similarly along height u will get x and 80-x. then c the sollution given by sahil

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NEETU MORWANI  (11 years ago)

by solving the equation we get x=70...where is the need to divide 70 by 2...???can anybody explain

Is this solution Helpfull? Yes | No (1)  

Sourav Saha  (11 years ago)

I think ans is 20.
a/h=8/10;
(60-x)^2 +x^2 + x^2 + (80-x)^2 = [10x/8]^2+[100-10x/8]^2

Is this solution Helpfull? Yes | No (1)  

sanjana  (11 years ago)

i got the question n also solution of ur sahil motwani but got stuck in last concept..
finally i got the eq. 100=2x*x+(60-x)*(60-x)+(80-x)*(80-x)
m i going rgt or not???

Is this solution Helpfull? Yes | No (4)  

venkatesh bollam  (11 years ago)

y should i divide 70 by 2

Is this solution Helpfull? Yes | No (1)  

THATI PAVAN KUMAR  (11 years ago)

it is 20 becz.....draw a square inside the triangle you got and maximise the obtained triangle with sides 80-x,x by differensiation making equals to zero.......u will end up with x=20

Is this solution Helpfull? Yes | No (2)  

loganand  (11 years ago)

here ladder forms hypotenuse(100m) with the wall(opp or adj side).
According to Pythagoras theorem we will get
X^2 + 60^2 = 100^2
=> X^2 = 6400
=> X = 80

Now ABC forms a triangle with side AB=80, BC=100, AC=60.
consider that a cude DEFG is inscribed in a triangle, such that vertice E lie on the side BC, and lines DG and FG lies on AB and AC respectively.

here size of cube will 30X40 = 120

Is this solution Helpfull? Yes | No   

shivendra pratap singh  (11 years ago)

make triangle abc in which ab is the perpendicular or we can say that is wall 60m and base bc let taken as x and hypotenuse is the ladder that is leaning against the wall so apply pyathagoras theorem
(10)^2-(60)^2=6400
so sqrt of 6400 is 80

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babu rao ganpat rao apte  (10 years ago)

well its a piece of cake u all are making it difficult....

we are given a rt triangle with base 60,,hyp=100..so third side is 80..

area=1/2*base*height...(A1) here base =60 height=80

now look at triangle from another veiw....
area=1/2*base*height

this time take hypotnuse as base of triangle...
from A1 we can calculate height

this is nothing but the diagnol of the biggest cube
calculate this...from which we can get the side...
answer will come out about 33.5

Is this solution Helpfull? Yes | No   

utkarsh rawal  (9 years ago)

if edge of cube is x, so we can say that,

tan(53.13) = x / (60-x)

3187.8 - 53.13x = x
so,
x = 58.89 m

Is this solution Helpfull? Yes | No   

Shubham Khandalkar  (8 years ago)

As RAVINDRA KUMAR YADAV stated the equation is 4x+3y-240=0. Now we have equal x and y for a square. Lets put z in place of x and y. => 4z + 3z = 240.... => 7z = 240.... => z = 240/7..... which is aprox 34.28

Is this solution Helpfull? Yes | No   

shikhar  (8 years ago)

let size of cube be x.
/ 1
/ 1 80-x
/ 1
/ 1 ------ 1
1 1 x
------------ 1
(60-x),x

80/60=x/60-x,x=34

Is this solution Helpfull? Yes | No   

Puja Kumari Shaw  (8 years ago)

Refer here for proper explanation..!!
http://www.examveda.com/if-a-ladder-is-100m-long-and-distance-between-bottom-of-a-ladder-and-wall-is-60m-what-is-the-maximum-size-of-the-cube-that-can-be-placed-between-1513/

Is this solution Helpfull? Yes | No (1)  

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