While calculating the side of a square 10 excess is made what is the percentage increase in its area

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Discussion :: Area - General Questions (Q.No.2)

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1. An error $2\%$ in excess is made while measuring the side of a square. What is the percentage of error in the calculated area of the square?
A. $4\%$	B. $2\%$
C. $4.04\%$	D. $2.02\%$

Answer: Option C

Explanation:

Solution 1

Refer formula

Percentage error in calculated area
$=\left(\dfrac{2^2}{100}+2×2\right)\%=4.04\%$

Solution 2

Error $=2\%$

Let correct value of the side of the square $=100$
Then, measured value $=100+2=102~~$(∵ $2$ is $2\%$ of $100$)

Correct area of the square $=100^2=10000$
Calculated area of the square $=102^2=10404$

Error $=10404-10000=404$

Percentage error $=\left(\dfrac{404}{10000}×100\right)\%=4.04\%$

Note: With the following variation, one can avoid calculation of $102^2$

Correct area of the square $=100^2$
Calculated area of the square $=102^2$

Error $=102^2-100^2$
$=(102-100)(102+100)=2×202=404$

Percentage error
$=\left(\dfrac{404×100}{100^2}\right)\%=4.04\%$

I don't get this - if i take the side as 10 - a 2 % error is 12- 10 - being the correct measure, squared is 10012 - the incorrect measure, squared is 144the error is 44so the percent change should be - 44/100 x 100 = 44 % ?

why does this give 44 % as the value - ?

Actually 2% error of 10 is not 12. it is 10.2,
Now u can calculate the correct answer .

Actually 2% error of 10 is not 12. it is 10.2,<br>Now u can calculate the correct answer .

if side is 10, error is 2% of 10 which is 0.2 and hence the side is 10.2

i have a question . how did 100 come there?please justify.with regards

carly

i have a question . how did 100 come there?please justify.with regards <p>carly</p>

see there 100 means we are taking that value for finding the actual area of the square

correct value of the side of the square is taken as 100 for ease of calculation. Any value can be used and answer will be same as we are calculating percentage.

Can any one explian me how the measured value = 100×(100+2)100=102 has been taken here.

<br>Can any one explian me how the measured value = 100×(100+2)100=102 has been taken here.

bcause 2%error is there

Here Two 100's will cancel. Then, remaining value will be (100+2). So 100+2=102

Let the actual value is xIf error is y% in excess, measured value = x(100+y)/100

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Discussion :: Area - General Questions (Q.No.2)

An error 2% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is:

[A].	2%
[B].	2.02%
[C].	4%
[D].	4.04%

Answer: Option D

Explanation:

100 cm is read as 102 cm.

A1 = (100 x 100) cm2 and A2 (102 x 102) cm2.

(A2 - A1) = [(102)2 - (100)2]

= (102 + 100) x (102 - 100)

= 404 cm2.

Percentage error =		404	x 100	%	= 4.04%
100 x 100

Ramesh said: (Mar 6, 2011)
Sir Percentage error is not understanding. Please solve the answer.

Sakshi said: (Mar 7, 2011)
We can also get the percentage by this. Percentage error = 404/100 = 4.04

Anbu said: (Dec 4, 2011)
(A2 - A1) = [(102)2 - (100)2] How it come? Please advise

Amrita said: (Dec 10, 2011)
To find out error we got to subtract it first.

Shreya Singh said: (Feb 3, 2012)
In this type of % some usefull idea is to take default no as 100 and in question 2% is error. Hence our no is 100 error no is 102. So solve further with square formula: Area= (side)* (side)

Mazher said: (Feb 8, 2012)
Why we are taking this three 100's ?

Meghna said: (Apr 8, 2012)
@anbu. Take the formula a^2-b^2 which is equal to (a+b)(a-b) ... so (102-100)(102+100)

Shikha said: (Apr 29, 2012)

Why are we dividing 401 by 100 two times and not one time?

Why it is not- (401*100) /100?

Pradyumna said: (Oct 16, 2012)
@Sikha. That is (404100) /(100100). Because we are finding the %error. Where 404 is change in area and (100*100) for original area.

Hasini said: (Sep 24, 2013)
Correct area = (100)^2. Measured area = (102)^2. So to get the excess area we have to subtract the incorrectly measured area by the correct area. (102)^2-(100)^2. (102+100)(102-100) . 202*2. = 404. So, 404/100. = 4.4%.

Srikanth said: (Oct 24, 2013)

Remember this formula x+y+(xy/100). For rectangle x and y are different, I mean length and breadth are different. Here is square so, only single element we can consider x and y as side of the square. So (+ for increase and "-" for decrease) 2+2+(2*2/100) = 404/100 = 4.04%. Lets check an example for rectangle if length increased 5% and breadth decreased 4% so the result is

5-4+(5*(-4))/100 = 0.8% over all decrease.

User said: (Dec 28, 2013)
@Sreekanth you are right. Thanks for sharing with us. And this seems to be very easy method for solving these kind of problem.

Bhavana said: (May 19, 2014)
Why are we taking 100 for this sum when it is not mentioned in the question. Please explain?

Aditi said: (Jun 22, 2014)
Why are we taking 100 for this sum when it is not mentioned in the question. Please explain?

Aarti said: (Jun 30, 2014)
Solution: x+y+xy/100 = 2+2+22/100 = 4.04.

Nitin said: (Jul 5, 2014)
%error = a+b+ab/100. a and b are +ve and -ve as per increment and decrement respectively.

Lipu said: (Sep 29, 2014)
Error % = (error/true value)100. So (404/100100)*100 = 4.04

Kasinath @Hyd said: (Oct 7, 2014)
Correct value is 100100. Measured value is 102102. Therefore ERROR Value is (102102)-(100100) = 404. Error% = (error value/ true value)100. => (404/100100)*100 = 4.04.

Engr. Md. Easir Arafat said: (Nov 23, 2014)
Let's the side to be 1. Here calculated (1+(2/100)) = 1.02. Hence the area becomes (1.021.02) = 1.0404 but the actual area was supposed to be (11) = 1. The difference = 1.0404-1.00 = 0.0404 = 4.04/100 = 4.04%. Note: Although taking only two decimals is conventional but in such types of small quantities we should take more to minimize the affect of error as much possible.

Sohel said: (Feb 14, 2015)
It can be also done as. Assume side of the square. Let S = 100 excess error is 2% i.e., 102. Now Area of the Square A = SS. A = 100100 = 10,000 cm2 (with out error) 1. A = 102-102 = 10,404 cm2 (with 2% excess error) 2. Difference b/w 1 and 2 is 404. i.e, 404/100 = 4.04%. Hope it will help you.

Mahesh said: (Jul 26, 2015)
Why you all are consider side of the square is 100. If we are tack original side of the square is 50. 2% error so side is 50*2/100 = 1. So side of square is 51. = (51)^2 - (50)^2 = (51+50) (51-50) = 101/100 = 1.01 answer. Please explain me.

Harsh said: (Sep 10, 2015)
Why is this method wrong? A = a^2; dA = 2ada; dA/A = 2*(da/a). We know da/a = 2%. Hence, dA/A = 4%. I don't seem to understand the reason why this is wrong? Can someone explain?

Harsh said: (Sep 10, 2015)

@Mahesh,

Difference in the area is indeed 101 but you must not divide it by 100. The area for your square was 2500 (50*50) and multiplying this by 100 (for percentage) gives you (101/2500)*100 = 4.04.

Abhishek Maurya said: (Jan 10, 2016)
Percentage error = X+Y+(XY)/100. So, => 2+2+(2*2)/100. = 4.04. Note : This method valid for only two values.

Danah Bader said: (Mar 26, 2016)
Exactly @Harsh. The method is wrong! I don't seem to understand the reason why this is wrong?

Pranjal said: (Apr 20, 2016)
The formula X + Y + (X*Y/100) is the best for square and rectangle.

Bhavna said: (Aug 4, 2016)
2% is the excess Let say area is 100 cm. Therefore, Wrong area is 100 + 2 cm. Right area is 100 cm. Wrong - Right = (102)^2 - (100)^2. 404. Error is - (excess/total area) i.e. 404/100 which gives 4.04 Now you can find the percentage by multiplying and dividing by 100. Ans -> 4.04%

Raju said: (Nov 19, 2016)
The formula X + Y + (X * Y/100) is the best for square and rectangle.

Sakshi said: (Feb 4, 2017)
Please explain the last step of the solution.

Arpita said: (Apr 29, 2017)
But it isn't given that error is made and the length is increased by 2cm. I mean 2%of 100 = 2. But then we can even subtract 2 from 100 which us 98 instead of adding that 2. Please help me.

Shivangi said: (Sep 2, 2017)

Let the actual side of the square be "a" units. then Actual area=a*a sq units 2% excess in side=102*a/100 (lets call this side "a1"). Excess Area =a1*a1=(102*a/100)*(102*a/100) =(2601*a^2)/2500 sq units. Now, error in area=Excess Area-Actual area =(2601*a^2)/2500-(a^2) sq units = (101a^2)/2500 sq units. Now percentage error=(error in area/actual area)*100 =(((101a^2)/2500)/a^2)*100 =101/25

= 4.04%.

Jobin said: (Apr 10, 2018)
Percentage error= ( Experimental value - theoretical value )/theoretical value 100. Therefore, Here percentage error= [(102)^2 - (100)^2]/(100)^2, = 404100/(100)^2.

Dwaipayan said: (May 26, 2019)
You are right, Thanks @Harsh.

Dada Khalandar said: (Jul 8, 2019)
How? Explain the answer please.

Tejasri Samala said: (Aug 28, 2019)
In order to find the percentage error, the formula is [ (xx) /100+2x]%.

Rohith said: (Nov 28, 2019)
We can also solve this is in 404/10.

Harshavardhan Reddy said: (Dec 19, 2019)
Use the formula {A+B+(AB/100)}. Here A=2 for side. For area A=B. 2+2+2*2/100=4.04.

Akil said: (Aug 15, 2022)
It is simple; Error is 2% so, take it 1.02. Now one side of a square is 'a'. Area = (a1.02)(a1.02), = (aa*1.0404). So, the total error in area = 4.04%.