Let original side of square be x.
Let Area of of square with original side be (x)²
Length increased by 7: x + 7
New are of square increased by (not to) 189: x² + 189
Equation:
(x+7)² = x² + 189 (increased BY 189)
x² + 14x + 49 = x² + 189
x² - x² + 14x = 189 - 49
14x = 140
14x/14 = 140/14
x = 10 inches, the original length of the side of square.
To check:
Original measurements:
(x inches)² = area
(10 inches)² = 100 squared inches
New measurements:
(10 inch + 7 inch)² = 100 sq. inch + 189 sq. inch
(17 inc)² = 289
289 sq. inches = 289 sq. inches
