# Aptitude - Area - Discussion

### Discussion :: Area - General Questions (Q.No.8)

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

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?