Question 64411
If the sides of a square are decreased by 3 cm, the area is decreased by 81 cm^2.  What were the dimensions of the original square?
Let the original side be: x
Then the area is:x^2
Then if we decreased it by 3 the new sides would be: x-3
The area of the original decreased by 81 is: x^2-81
The area of the new square is:(x-3)^2
 {{{(x-3)^2=x^2-81}}}
{{{x^2-6x+9=x^2-81}}}
{{{x^2-x^2-6x+9=x^2-x^2-81}}}
{{{-6x+9=-81}}}
{{{-6x+9-9=-81-9}}}
{{{-6x=-90}}}
{{{-6x/-6=-90/-6}}}
{{{x=15}}}
The original sides were 15 cm.
Sanity Check:
If the original sides were 15 cm, the area would be 15^2=225.
If the new sides were 15-3=12 cm, the area would be 12^2=144
If we subtract the two areas we get: 225-144=81
Happy Calculating!!!