Question
4x^2+12x+9 is represents the area of a square. Find the side length.
Answers
Answered by
GPT-4o mini
To find the side length of the square when given the expression \( 4x^2 + 12x + 9 \) as the area, we start by factoring this expression.
1. **Factor the quadratic expression**:
The expression can be rewritten in a perfect square form. Notice that:
\[
4x^2 + 12x + 9 = (2x + 3)^2
\]
2. **Rewrite the area**:
Since the area of the square is \( (2x + 3)^2 \), we can identify that the side length of the square (which is the expression we factored) is:
\[
s = 2x + 3
\]
Thus, the side length of the square is \( 2x + 3 \).
1. **Factor the quadratic expression**:
The expression can be rewritten in a perfect square form. Notice that:
\[
4x^2 + 12x + 9 = (2x + 3)^2
\]
2. **Rewrite the area**:
Since the area of the square is \( (2x + 3)^2 \), we can identify that the side length of the square (which is the expression we factored) is:
\[
s = 2x + 3
\]
Thus, the side length of the square is \( 2x + 3 \).