Question

If the width and length of a rectangle are both increased by 10%, by what percent does
the area of the rectangle increase? By what percent does the perimeter of the rectangle
increase?

Answer 1

Answer:

The area is increased by 21% and the perimeter by 20%

Solution:

Consider a rectangle of lenght $x$ and width $y$, its area is $xy$ and its perimeter is $2x+2y$. When a number $n$ is increased by 10%, its new value is equal to $(1+10\%)n = 1.1n$. So, our rectangle will have a new lenght of $1.1x$ and a new width of  $1.1y$, thus an area of $1.1x \cdot 1.1y = 1.21xy$. This tell us the area was increased by 21%.

The same is valid for the perimeter, which went from $2(x+y)$ to $2(1.1x+1.1y)=2.2(x+y)$, giving us an increase of 20%.