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A rectangle's width is 5 feet less than its length. Write a quadratic function that expresses the rectangle's area in terms of its length.

A. [tex]A(l) = l^2 + 5l[/tex]
B. [tex]A(l) = l^2 - 5l[/tex]
C. [tex]A(l) = lw[/tex]
D. [tex]A(l) = w(w + 5)[/tex]

Sagot :

GinnyAnswer
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]
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