The length of the longer side of rectangle $r$ is $10$ percent more than the length of a side of square $s.$ the length of the shorter side of rectangle $r$ is $10$ percent less than the length of a side of square $s.$ what is the ratio of the area of rectangle $r$ to the area of square $s? $ express your answer as a common fraction.

Let
x> length of the side of a square

[area of a square]=x*x> x²

[area of rectangle]=[shorter side]*[longer side]
[shorter side]=0.90 x> (is 10% percent less than the length of a side of square)
[longer side]=1.10x> (is 10% percent more than the length of a side of square

[area of rectangle]=(1.10x)*(0.90x)> 0.99x²

[the ratio of the area of rectangle to the area of square]=0.99x²/x²=0.99

the answer is
the ratio of the area of rectangle to the area of square is 0.99