Answer :
To find the area of a rectangle in terms of its length, we need to use the relationship between the length and the width provided in the problem.
1. Let the length of the rectangle be [tex]\( l \)[/tex].
2. According to the problem, the width ([tex]\( w \)[/tex]) is 5 feet less than the length. Therefore, we can express the width as:
[tex]\[ w = l - 5 \][/tex]
3. The area ([tex]\( A \)[/tex]) of a rectangle is calculated by multiplying the length by the width:
[tex]\[ A = l \times w \][/tex]
4. Substitute the expression for the width into the equation for the area:
[tex]\[ A = l \times (l - 5) \][/tex]
5. Simplify this expression:
[tex]\[ A = l \times (l - 5) \][/tex]
[tex]\[ A = l^2 - 5l \][/tex]
Thus, the quadratic function that expresses the rectangle's area in terms of its length is:
[tex]\[ \boxed{A(l) = l^2 - 5l} \][/tex]
So, the correct answer is:
B. [tex]\( A(l) = l^2 - 5l \)[/tex]
1. Let the length of the rectangle be [tex]\( l \)[/tex].
2. According to the problem, the width ([tex]\( w \)[/tex]) is 5 feet less than the length. Therefore, we can express the width as:
[tex]\[ w = l - 5 \][/tex]
3. The area ([tex]\( A \)[/tex]) of a rectangle is calculated by multiplying the length by the width:
[tex]\[ A = l \times w \][/tex]
4. Substitute the expression for the width into the equation for the area:
[tex]\[ A = l \times (l - 5) \][/tex]
5. Simplify this expression:
[tex]\[ A = l \times (l - 5) \][/tex]
[tex]\[ A = l^2 - 5l \][/tex]
Thus, the quadratic function that expresses the rectangle's area in terms of its length is:
[tex]\[ \boxed{A(l) = l^2 - 5l} \][/tex]
So, the correct answer is:
B. [tex]\( A(l) = l^2 - 5l \)[/tex]
