A geometry problem by Vaibhav Raj

Let side = 100. Increase 1% =101. Area = 10201 = 2.01% increased

Let the side of square = x. Thus, area A= x^2. Now when side is increased by 1%, The new side is x+x/100 = 101x/100. Thus, the new area is , A'= (101x/100)^2 = 10201x^2 /10000. The area ratio = A'/A = 10201/10000. The percentage area ratio = A'/A * 100% = 10201/100 =102.01%. Thus percentage increased= A'/A * 100% - 100%= (102.01-100)% = 2.01%

$\large \color{#D61F06}This~problem~is~a~piece~of~ice~cream!$

let $A_1$ be the area of the original square and $A_2$ be the area of the larger square, then

$\dfrac{A_1}{A_2}=\dfrac{1^2}{1.01^2}=\dfrac{1}{1.0201}$

It follows that, $A_2=1.0201A_1$

$\%~increased=(1.0201-1)(100\%)=2.01\%$

Let $s$ be the side length of this square. The new area of the square is $(1.01s)^2$ , or $1.0201s^2$ . So, the answer is $\boxed{2.01 \% }$ .

Considering side increased by 1 % ,so area of 100 cm length of square will be 10000, get increased to 10201 that is 2.01 % Ans K.K.GARG,India

Since they are similar polygons,

$\frac{A_1}{A_2}=$ $\frac{a^2}{(1.01a)^2}$ $=$ $\frac{1}{1.0201}$

$1.0201A_1=A_2$

% $increased=$ $(1.0201-1)(100)=2.01$ %

Another way of attacking problems like this is to set a value for a, and the best value is 1, so we let the side of the original square to be 1 unit, then the larger side is 1.01(1) = 1.01 unit

area of original square = 1

area of bigger square = (1.01)^2 = 1.0201

% increased in area = (1.0201 - 1)(100) = 2.01%

Total area = 1.01 x 1.01 = 1.0201
Area increase 0.0201 = 2.01 %

Let each side of the square is 1cm long. Then area of the square is 1cm sq. If we increase each side of the square by 1%, then each side of the square is 1.01cm resulting the area of the square to 1.0201cm sq. When we take the difference of the area of the square as a result of 1% increment on its each side, we get 0.0201. Simply putting these in percentile we get 2.01%.

I let the the sides of the smaller square equal 100, and the larger square equal 101. The area of the smaller square = 100 100 = 10,000. The area of the larger square = 101 101 = 10,201. The difference is 201. 201/10000 = .0201 or 2.01%.

For 100 100(10000) it becomes 101 101(10201)

So, 10000 is increased by 201 1 is increased by 201/10000 100 is increased by 201*100/10000=2.01

let side of the square be a side of the square increased by 1% so side becomes 1.01a area of the square becomes (1.01a)^2=1.0201a^2 area increased in %= ((a^2)-(1.0201a^2))*100/a^2=2.01%

Lets take side of square a is 100 and area is a^2. so 10000. If side increase by 1% is 101. so are 10201. Square without increase is 10000 & after increase is 10201. Difference 201(increased). To find percentage we have to get in term of hundred, for that we can remove two points in 10201/100(to get value in hundreds) it 102.01. Increased square value 2.01

a= %inc in l b=%inc in b a+b+(a*b)/100

use a+a+(a.a/100) % where a= % increased

If the square initially has a side length of 'A' then after the increase the side lengths are now (A+A/100). Initially, the square has an area of A^2, but after the increase the area is now (A+A/100)^2.

This means that after the increase the square now has an area of A^2 + (2A^2)/100 + (A^2)/10000. Now initially, the square had an area of A^2, therefore to find the increase as a decimal multiplier, divide through by A^2. This gives: 1+2/100+1/10000.

We now multiply this by 100 to get a value of the area of the new square as a percentage of the 'old square' size. Hence we get: 100%+2%+0.01%= 102.01%. The 'old square' was 100% so to find % increase we can simply subtract 100% from 102.01% , which is 2.01%.

Therefore 2.01% is the solution.

\frac { { S } { 2 } }{ { S } { 1 } } =\frac { { A } { 2 } }{ { A } { 1 } } \ *where;\quad { S } { 2 }={ 1.01(S } { 1 })\ { \left[ \frac { { 1.01(S } { 1 }) }{ { S } { 1 } } \right] }^{ 2 }=\frac { { A } { 2 } }{ { A } { 1 } } \ *cancel\quad { S } { 1 }\ { (1.01) }^{ 2 }=\frac { { A } { 2 } }{ { A } { 1 } } \ 1.0201({ A } { 1 })={ A }_{ 2 }\ \therefore \quad The\quad area\quad is\quad increased\quad by\quad 2.01%\quad of\quad the\quad original\ \ \