A rectangle with an area of x^2+4x+3
 is modeled using algebra tiles.

First row has 4 parts. First part is a rectangle and other three parts are small squares. Second row has 4 parts. First part is a bigger square and other three parts are rectangles. The key at the right side shows a small square equals to 1, a rectangle equals to x, bigger square equals to x squared.

What are the dimensions of the rectangle in terms of x?

The given area of the rectangle is \(x^2 + 4x + 3\). This quadratic expression can be factored to help determine the dimensions of the rectangle. Let's factor the quadratic:

\[ x^2 + 4x + 3 = (x + 1)(x + 3) \]

The dimensions of the rectangle are represented by the factors of the quadratic expression. Therefore, the dimensions of the rectangle in terms of \(x\) are \(x + 1\) and \(x + 3\). 

The algebra tiles representation supports this factorization:
- The larger square corresponds to \(x^2\).
- The four rectangles represent the \(4x\) term, likely adding up to the total length of one of the sides.
- The three smaller squares represent the constant term +3.

This arrangement reaffirms the dimensions \( (x + 1) \times (x + 3) \).

A rectangle with an area of x^2+4x+3 is modeled using algebra tiles. First row has 4 parts. First part is a rectangle and other three parts are small squares. Second row has 4 parts. First part is a bigger square and other three parts are rectangles. The key at the right side shows a small square equals to 1, a rectangle equals to x, bigger square equals to x squared. What are the dimensions of the rectangle in terms of x?

Learn how to find the dimensions of a rectangle when its area is represented by the quadratic expression x^2 + 4x + 3. This problem involves factoring quadratic expressions and understanding algebra tile models. Suitable for students in Grades 7-9.

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