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.