Mr. lumen replaced a square window with a rectangular one. the new window is 3 ft. wider and 2 ft. higher than the square one. it has an area of 42 ft. how long was a side of the original square.

Let the length and width of the square window be x ft.
the new dimensions are:
length=(x+3) ft and width=(x+2) ft
the area will be:
A=length*width
thus
A=(x+3)(x+2)=42
x^2+5x+6=42
x^2+5x-36=0
factoring the above we get:
(x-4)(x+9)=0
thus
x=4 or x=-9
hence we take x=4 since there is n negative dimension.
Thus the original dimension of the square was 4 ft by 4 ft.