Question 999099
let x = the length of the original side of the square plot.


one side is increased by 30 feet and becomes x + 30.
the other side is decreased by 10 feet and becomes x - 10


the area of the rectangular foundation is 2100 square feet.
length * width = area
(x+30) * (x-10) = 2100
multiply out the factors to get:
x^2 - 10x + 30x - 300 = 2100
combine like terms to get:
x^2 + 20x - 300 = 2100
subtract 2100 from both sides of this equation to get:
x^2 + + 20x - 2400 = 0
factor this quadratic equation to get:
(x+60) * (x-40) = 0
solve for x to get:
x = -60 or x = 40
x can't be negative, so x = 40


the area of the original square foundation was x*x which becomes 40*40 = 1600 square feet.


the original foundation was 40 by 40.
the new foundation became 70 by 30


40 * 40 = 1600 square feet.
70 * 30 = 2100 square feet.


the original side length was 40.
the rectangular side lengths were x+30 and x-10.
x+30 = 70
x - 10 = 30


everything checks out ok.