If the side of square increase by 25% by what percentage does the area of the square increase?

1 Answer
Apr 16, 2018

I tried this:

Explanation:

Consider a square of side length #a#, the area will be:

#A=a*a=a^2#

now let us increase the length to #a+0.25a# so that the new area will be:

#A'=(a+0.25a)^2=(1.25a)^2=1.5625a^2#

But we remember that #A=a^2# so substituting we get:

#A'=1.5625A# or #=A+0.5625A# corresponding to a #56.25%# increase.

Consider an example:
let the original side be #a=10#
so we get that the area is:

#A=10*10=100ua#

increase the length to #10+0.25*10=12.5#
The new area will become:

#A'=(12.5)^2=156.25ua#