To solve this problem step-by-step, let's break it down:
1. Understanding the Problem:
- We have a rectangle.
- The length [tex]\( l \)[/tex] of the rectangle is 5 less than the width [tex]\( w \)[/tex].
2. Expressing the Length in Terms of the Width:
- Given that the length [tex]\( l \)[/tex] is 5 units less than the width [tex]\( w \)[/tex], we can write:
[tex]\[
l = w - 5
\][/tex]
3. Finding the Area of the Rectangle:
- The area of a rectangle is found by multiplying the length by the width.
- Therefore, the area [tex]\( A \)[/tex] can be given by:
[tex]\[
A = \text{length} \times \text{width} = (w - 5) \times w
\][/tex]
- Simplifying this expression, we get:
[tex]\[
A = w(w - 5)
\][/tex]
4. Identifying the Correct Expression:
- Given choices:
- [tex]\( w(w-5) \)[/tex]
- [tex]\( 2 w-5 \)[/tex]
- [tex]\( w(5-w) \)[/tex]
- [tex]\( l(w-5) \)[/tex]
- The correct expression matches our derived formula:
[tex]\[
w(w - 5)
\][/tex]
So, the correct choice for the expression to find the area is:
[tex]\( w(w-5) \)[/tex]
