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John is building a rectangular pen for his sheep. The length of the pen is 5 more than 8 times the width of the pen.

Complete an equation for the area of the pen, where [tex]\( w \)[/tex] is the width of the pen.

[tex]\[ A = 8w^2 + 5w \][/tex]



Answer :

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]