Answered

Discover the answers you need at Westonci.ca, where experts provide clear and concise information on various topics. Our platform provides a seamless experience for finding precise answers from a network of experienced professionals. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

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]
Thanks for using our platform. We're always here to provide accurate and up-to-date answers to all your queries. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.