Aptitude - Area - Discussion
Discussion Forum : 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?
Answer: Option
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 |
Discussion:
39 comments Page 2 of 4.
Navaneeth said:
9 years ago
If that person walked along edges. Approximately, what was the percent wasted by walking along the edges?
Please give me the answer.
Please give me the answer.
Faziha said:
9 years ago
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%.
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%.
(6)
Suresha E S said:
1 decade ago
AC = root (2x).
Root of 2 = 1.41.
But where did the root of x disappeared?
Root of 2 = 1.41.
But where did the root of x disappeared?
(1)
AK Nirala said:
1 decade ago
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).
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).
Amit Kumar Swain said:
1 decade ago
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).
Edges are 7 then 7-5=2 (Different).
(2/7)=(x/100).
Solve x=28.57142857 (i.e approximately 30).
Namrata said:
1 decade ago
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?
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?
Namrata said:
1 decade ago
AC = root (2x).
Root of 2 = 1.41.
But where did the root of x disappeared?
Root of 2 = 1.41.
But where did the root of x disappeared?
Anjali said:
1 decade ago
How it came (.59x)m?
Maaz said:
1 decade ago
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%.
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%.
(2)
Pragnya said:
1 decade ago
Please can anyone explain the last step in the solution? Which formula has been used there?
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