Aptitude - Area - Discussion

8. 

A man walked diagonally across a square lot. Approximately, what was the percent saved by not walking along the edges?

[A]. 20
[B]. 24
[C]. 30
[D]. 33

Answer: Option C

Explanation:

Let the side of the square(ABCD) be x metres.

Then, AB + BC = 2x metres.

AC = 2x = (1.41x) m.

Saving on 2x metres = (0.59x) m.

Saving % = 0.59x x 100 % = 30% (approx.)
2x


P.Bharathi said: (Oct 2, 2010)  
Saving on 2x metres = (0.59x) m.

How this step arise ? Please explain me clearly.

Sneha G.B said: (Jan 4, 2011)  
saving 2x meters means......

2x-1.41x=0.59x

Ashu said: (Jan 15, 2011)  
Use pyth. Theorem so you get the value of diagonal ac that is root 2 or 1. 41x. Now the distance saved by walking diagonally is 2x-1.41x i.e. 0.59x.

Sandeep said: (Jan 27, 2011)  
Any other way to solve this problem ?

Kaps said: (Jun 11, 2011)  
Easiest way told by ashu.

J.Gopikrishna said: (Jun 15, 2011)  
Please tell easy way to solve the problem?

Suresh said: (Jun 17, 2011)  
How Ac=root of2X?

Sumit said: (Jun 30, 2011)  
1.41*1.41x=2x

Kb3 said: (Jul 17, 2011)  
Let abcd be the square with each side of the square = 8m then

ab+bc=2 x 8= 16m
ac= sqrt(16)=4m

solving = 16-4= 12m

Hence, 4/12*100=33.33 approx.

Abhi said: (Nov 28, 2011)  
IN a sqare let us assume the sides be 3, 4 units then the diagonal will be 5 by pythagorus theorem ..thus 2 units are saved (7-5) .. total saved %=2/7*100 =28.57 i e 30%

King Cobra said: (Dec 14, 2011)  
Hey KB3. You are wrong. Solve by PYTHOGORUS theorem,,

From the fig shown above.
Root of AB square + BC square = AC.

Scott said: (Jul 13, 2012)  
From the fig shown above.
Root of AB square + BC square = AC.

Ajay said: (Jul 26, 2012)  
Lets say sides of square is 10 and let diagonal be x therefore by Pythagoras theorem.

X2 = (10) 2 + (10) 2 = 200.

X = 10root2 = 10 x 14.1 (root2 = 1.412).

Therefore 20 - 14.1 = 5.9.

5.9/20 = 0.30 i.e. approx 30%.

Arpit Jain said: (Sep 1, 2012)  
Hey kb3 u have used wrong formula
its (square root of 2)*(X)
ab+bc = 16m
sqrt(2)*8 = 11.313
16-11.313 = 4.68
(4.68*100)/16 = 29.28%

Sudhakar said: (Jul 12, 2013)  
Suppose ab = 2, ac = 2 then ab+ac=4.

Diagonal bc = ?

Pythagoras Proof bc^2 = ac^2+ab^2 (here ^2 means square).
bc^2= 4+4.
bc=(square root of 8).
bc= 2.83.

Gain = 4-2.83 = 1.17.

Gain(%) = (1.17/4)*100 = 29.28%.

Atul Jain said: (Oct 28, 2013)  
Let we have a square. starting from left top to right A,B,C,D.

After that make a diagonal AC.

As we know that we don't know the side of square then we assume x.

Now we start to run from A to C then path is AB+BC and its value,
is x+x = 2x.

Then equation is AB+BC = 2x.

Now the diagonal of the square formula is,
d = square root of 2 x.
d = 1.41x.

Saving per cent is ((2x-1.41x)/2x)*100 .

29.5. approx 30.

Suraj said: (Mar 23, 2014)  
How the each side of square is 1m?

Lakshya said: (Sep 20, 2014)  
Why should we have to multiply 0.59x/2x by 100? somebody please help me.

Anu said: (Sep 23, 2014)  
What is that 1.41?

Pragnya said: (Jan 9, 2015)  
Please can anyone explain the last step in the solution? Which formula has been used there?

Maaz said: (Jan 22, 2015)  
Simple go for the formulas of Area of Square. There are two formulas:

1) Area of Square = (Sides)2.
2) Area of Square = 1/2 (Diagonals)2.

Let 'S' is a side of square we know that all the sides of a square is equal. By first Formula Area will be S^2. Now putting this S^2 in 2nd Formula. We got the diagonal.

By second formula:

S^2 = 1/2(Diagonal)^2.

Taking square root on both sides.

Square root of 2*S = Diagonal.

Now we have to find Diagonal.

Diagonal = 1.414S(Square root of 2 = 1.414).

So The difference between Diagonal and Edges is:

2S-1.414S = 0.59S.

Percentage saved not by walk on edges = Extra Walk/Total Walk*100.

= 0.59S/2S*100 = 30%.

Anjali said: (Mar 6, 2015)  
How it came (.59x)m?

Namrata said: (Jun 10, 2015)  
AC = root (2x).
Root of 2 = 1.41.

But where did the root of x disappeared?

Namrata said: (Jun 10, 2015)  
I will go with @Ajay's method where he took side as 10 instead of variable.

Because is you take variable you go land up in confusion.

AC = Root of (2x).

Root of 2 = 1.41.

But what about root of x?

Amit Kumar Swain said: (Jun 29, 2015)  
According to Pythagoras the side are 3&4 or diagonal 5.

Edges are 7 then 7-5=2 (Different).

(2/7)=(x/100).

Solve x=28.57142857 (i.e approximately 30).

Ak Nirala said: (Aug 1, 2015)  
You (Amit) choose the sides of a rectangle not SQUARE.

EXAMPLE METHOD.

According to Pythagoras FOR SQUARE the sides are 2 & 2 or diagonal 2*sqrt(2) = 2*1.141 = 2.828 {where sqrt(2) = 1.141}.

Edges are 2+2 then 4-2.828 = 1.172 (Difference).

(1.172/4)*100 = 29.3 = 30 approx.

Simple method:

Edge of square let be x.

Then diagonal of square will be 2 sqrt(x).

Edge distance - Diagonal distance (difference).

2x-2sqrt(x) = x (2-sqrt(2)) = (2-1.414)x = 0.586x.

%AGE.

(0.586x/2x)*100 = (0.586/2)*100 = 29.3 (30 approx).

Suresha E S said: (Sep 22, 2015)  
AC = root (2x).

Root of 2 = 1.41.

But where did the root of x disappeared?

Faziha said: (Oct 2, 2016)  
We have to find saving distance from A to C.
First, from edges the distance we have to calculate.
So let's take side of a square as X
So for A to C.
We have to cross A to B then B to C.
So, X + X = 2X.
If we travel diagonally means the distance took is root of 2 multiplied by X.
So, saving will b 2X - root 2 X.
So (2.00 - 1.41) X = 0.59 X.
Saving % is 0.59X/2X * 100 = 30%.

Navaneeth said: (Feb 12, 2017)  
If that person walked along edges. Approximately, what was the percent wasted by walking along the edges?

Please give me the answer.

Senthil said: (May 19, 2017)  
@Amit kumar. How the edges are 7?

Ramakanth said: (Jul 24, 2017)  
Please tell me an easy way to solve the problem with the clear explanation.

Rahul said: (Aug 17, 2017)  
let us assume the side of square is 10 cm.
In a square all sides are equal.

To find the diagonal of a square we can use the following formula= Squareroot of (2*(side^2)).

In this case= Square root of (2*(10^2)) = 14.142.
Distance Traveled=14.142.
Distance if used the edge of the square= 10*2= 20.
Saving=20-14.142=5.858.
Saving in %=5.858/20 =30%.

Prajakta said: (Oct 3, 2018)  
Savings on 2xmeters = (0.59x)meter how?

Riya said: (Feb 7, 2019)  
@All.

Along the edges, that means more than one side, so how come it has been decided that it is only 2 sides? Solution has been given only for 2 sides. Why?

Why it can't be 4 sides?

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