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Answer:
The dimensions of the wall are 100 ft x 100 ft
Step-by-step explanation:
we know that
The perimeter of a rectangular wall is
where
x is the length
y is the width
we have
so
simplify
----> equation A
The area of a rectangular wall is equal to
----> equation B
substitute equation A in equation B
This is the equation of a vertical parabola open downward (because the leading coefficient is negative)
The vertex represent a maximum
Convert the quadratic equation in vertex form
Factor -1
Complete the square
Rewrite as perfect squares
----> equation in vertex form
The vertex is the point (100,10,000)
The x-coordinate of the vertex represent the length of the wall for a maximum area
so
Find the value of y
equation A
therefore
The dimensions of the wall are 100 ft x 100 ft