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:
38 comments Page 2 of 4.
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:
10 years 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?
Anu said:
1 decade ago
What is that 1.41?
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