I got 64 square feet.
My work is shown in the image.
For possible questions:
1: you can find x+7 and x-2 because the sides of the square can be measured as x, and x+7 means 7 more than the original; x-2 means 2 less than the original.
2: solved via factoring. Not sure if you've learned it or not.
3: reject the negative numbers because you can't have negative sides in a square.
Area of rectangle is multiplication of length and width.
Original area of square will be 64 square feet.
Let us consider the each side of square is x feet.
Since, one dimension is increased by 7 feet and the other is decreased by 2 feet . then, it become a rectangle have length (x + 7) and width (x - 2) feet.
Area of resulting rectangle = (x + 7)(x - 2)
[tex](x + 7)(x - 2)=90\\\\x^{2} +5x-104=0\\\\x^{2} +13x-8x-104=0\\\\x(x+13)-8(x+13)=0\\\\(x-8)(x+13)=0\\\\x=8,x=-13[/tex]
Since, length can not be negative. So x = 8 feet
Original are of square = [tex]x^{2} =8^{2}[/tex]
= 64 square feet
Learn more:
https://brainly.com/question/23148123
