A geometry problem by Manish Mayank

Let the side of the square be x,

It is given that,

Length of Rectangle R = x + 10/100 * x

                                       = 110x/100 .......................(1)

Width of Rectangle R = x - 10/ 100 * x

                                     = 90x / 100 ...........................(2)

from (1) and (2)

Ar R = L * W = 110x/100 * 90x/ 100

                  = 99x^2 / 100

Ar S = x^2

R : S =R/s = 99x^2/100 / x^2

     = 99/100 or 99: 100

It's Easy.

$\large{S=a^2}$

where: $a:\space$ side of the square

$\large{R=L*W}$

where:

$L:\space$ length of the Rectangle

$W:\space$ Width of the Rectangle

given that:

$\large{L=110\% a=1.1a}\space$

$\large{W=90 \% a=0.9a}\space$

then

$\large{R=1.1a \times 0.9a =0.99a^2}$

$\large{R:S = 99:100}$

Just assume a length and breath rectangle.I assumed length and breath both 10. Its area will be 10x10=100 . After this length became 11 and breath became 9 . So the area of new triangle will be 11x9=99. So ratio is 99:100.

Taking 10% more length of rectangle and width 10 % less, considering 10 as length and width of square,areas are 99 and 100 ,so ,ratio of R:S is 99/100 Ans.

K.K.GARG,India

Let, the side of the square is y. So, length and width of the rectangle is 1.1y and 0.9y respectively. Hence, the ratio is (1.1y)(0.9y) : y.y i.e. 99:100

Guess the side of the square is 100. So he rectangular has 110 height and 90 wight. Area of R=110 90=9900 & S=100 100=10000. So R:S=9900/10000=99:100

Let x the side of square. Then, we have the sides of rectangle 1,1x and 0,9x. So, the ratio of the areas R/S = 1,1*0,9 * x²/x² = 0,99 = 99/100

If side of a square=x, then Rectangle's Length= 1.1x , Width=0.9x

So Area of Rectangle/Area of Square =(1.1x*0.9x)/x^2 =0.99=99/100

area of square = S^2 area of rectangle = 1.1S x 0.9S = 0.99(S^2) Ratio = (0.99(S^2)) : (S^2) = 99 : 100

If a be the side of a square then the length of the rectangle is 11/10 a and width of rectangle is 9/10 a. Area of the rectangle is 99/100 a a and area of the square is a^2. Therefore the ratio of r/s is 99/100.