To find the equation for the area [tex]\( A \)[/tex] of the rectangular pen, we need to use the given information that the length [tex]\( L \)[/tex] of the pen is 5 more than 8 times the width [tex]\( w \)[/tex].
1. First, express the length [tex]\( L \)[/tex] in terms of the width [tex]\( w \)[/tex]:
[tex]\[
L = 8w + 5
\][/tex]
2. Next, remember that the area [tex]\( A \)[/tex] of a rectangle is given by the product of its length and width:
[tex]\[
A = L \times w
\][/tex]
3. Substitute the expression for [tex]\( L \)[/tex] into the area formula:
[tex]\[
A = (8w + 5) \times w
\][/tex]
4. Distribute [tex]\( w \)[/tex] to both terms in the parentheses:
[tex]\[
A = 8w^2 + 5w
\][/tex]
So, the equation for the area of the pen in terms of the width [tex]\( w \)[/tex] is:
[tex]\[
A = 8w^2 + 5w
\][/tex]
Thus, the completed equation for the area of the pen is:
[tex]\[
A = \boxed{8}w^2 + \boxed{5}w
\][/tex]
