Final answer:
To show that x² + 4x = 3 using the area of square ABCD (7 cm²), we set up the equation (x + 2)² = 7 cm². Expanding and simplifying this equation results in x² + 4x - 3 = 0, which, after adding 3 to both sides, shows that x² + 4x indeed equals 3.
Step-by-step explanation:
To show that x² + 4x = 3 using the area of square ABCD, which is 7 cm², we need to use algebraic methods and the properties of squares. Given that the length of one side of the square is composed of two segments totaling x cm + 2 cm, we can set up an equation to represent the square's area.
The area of a square is found by squaring its side length (a · a = a²), so for square ABCD with side lengths composed of x + 2 cm, the equation would be:
(x + 2) · (x + 2) = 7 cm²
Expanding the left side of the equation, we get:
x² + 4x + 4 = 7
Subtracting 7 from both sides gives us:
x² + 4x + 4 - 7 = 0
Thus,
x² + 4x - 3 = 0
So, we have demonstrated that by knowing the area of the square, and using simple algebra, x² + 4x indeed equals 3.