Question

question 8 of 10
a rectangles width is 6 feet less than its length. write a quadratic function that expresses the rectangles area in terms of its length.

a. ( a(l) = l^2 - 6l )
b. ( a(l) = lw )
c. ( a(l) = l - 6 )
d. ( a(l) = l^2 + 6l )

Explanation:

Step1: Define variables

Let \( l \) be the length of the rectangle. The width \( w \) is 6 feet less than the length, so \( w = l - 6 \).

Step2: Recall area formula for rectangle

The area \( A \) of a rectangle is given by \( A = l \times w \).

Step3: Substitute width into area formula

Substitute \( w = l - 6 \) into the area formula: \( A(l)=l\times(l - 6) \).

Step4: Expand the expression

Using the distributive property \( a(b - c)=ab - ac \), we get \( A(l)=l^{2}-6l \).

Answer:

A. \( A(l) = l^2 - 6l \)