Find the area of rectangle if the length is 5 more than thrice the width

Let's define the variables to solve this problem:

- Let \( w \) represent the width of the rectangle.
- The length of the rectangle is 5 more than thrice the width. Therefore, the length \( l \) can be expressed as:

\[
l = 3w + 5
\]

The area \( A \) of a rectangle is given by the formula:

\[
A = l \times w
\]

Substitute the expression for \( l \) into the area formula:

\[
A = (3w + 5) \times w
\]

Now, expand and simplify:

\[
A = 3w^2 + 5w
\]

The area of the rectangle in terms of its width \( w \) is:

\[
\boxed{3w^2 + 5w}
\]

If you know the width or want to explore further, let me know!

### Related Questions:

1. What is the perimeter of the rectangle if the width is known?
2. If the area is given, how do we find the width and length?
3. How would the formula change if the length were instead 5 less than thrice the width?
4. Can we express the dimensions of a square in a similar way?
5. What happens to the area if the width is doubled?

### Tip:
When forming equations from word problems, carefully translate phrases like "5 more than thrice" into mathematical expressions.

Discover how to calculate the area of a rectangle when the length is 5 more than thrice the width. This problem involves applying geometric and algebraic principles to find the area formula. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation