he length of a certain rectangle is 3 units more than double its width, *w*. Express the area of the rectangle in terms of *w*.

To express the area of the rectangle in terms of its width \( w \):

1. **Length**: The length of the rectangle is given as "3 units more than double its width". This can be expressed as:
   \[
   \text{Length} = 2w + 3
   \]

2. **Area**: The area \( A \) of a rectangle is calculated by multiplying its length by its width:
   \[
   A = \text{Length} \times \text{Width}
   \]

   Substituting the expressions:
   \[
   A = (2w + 3) \times w
   \]

3. **Simplify**:
   \[
   A = 2w^2 + 3w
   \]

Thus, the area of the rectangle in terms of \( w \) is:
\[
A(w) = 2w^2 + 3w
\]

Would you like more details or have any questions?

Here are 5 related questions to expand on this topic:

1. If the width \( w \) is 4 units, what is the area of the rectangle?
2. What is the perimeter of the rectangle in terms of \( w \)?
3. How would the area formula change if the length was "5 units more than triple its width"?
4. What is the width \( w \) if the area of the rectangle is 50 square units?
5. How do you find the dimensions of the rectangle if the area is given?

**Tip:** When working with quadratic expressions, factorization can sometimes help in finding the roots, especially if you're solving for the variable.

The length of a certain rectangle is 3 units more than double its width, w. Express the area of the rectangle in terms of w.

Learn how to express the area of a rectangle where the length is 3 units more than double the width w. This algebra and geometry problem walks you through using quadratic equations to derive the formula for the area, A(w) = 2w^2 + 3w. Suitable for students in Grades 8-10.

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