Answer :
Maximum area of rectangular park that can be enclosed using 5 feet long concrete barriers is equals to 40,000 square feet.
What is rectangle?
" Rectangle is defined as quadrilateral whose opposite sides are parallel and congruent with one of the angle equals to 90°."
According to the question,
Length of the concrete barrier = 5feet
Number of barriers = 160
Total length of barriers = 160 × 5
= 800 feet
'l' represents the length of the rectangular park
'w' represents the width of the rectangular park
'A' represents the area of the rectangular park
Perimeter of the Rectangular park = 2 ( length + width)
⇒800 = 2(l + w)
⇒ l + w = 400
⇒ w = 400 - l
Area of the rectangular park = length × width
⇒ A = l × ( 400 - l )
⇒A = 400l - l²
⇒[tex]\frac{dA }{dl} = 400 -2l[/tex]
⇒ [tex]\frac{d^{2} A}{dl^{2} }=-2 < 0[/tex]
Therefore , maximum function.
[tex]\frac{dA }{dl} =0[/tex]
⇒[tex]400 -2l =0[/tex]
⇒[tex]l= 200[/tex]
and
[tex]w = 200[/tex]
Maximum area that can be enclosed = 200 × 200
= 40,000 square feet.
Hence, maximum area of rectangular park that can be enclosed using 5 feet long concrete barriers is equals to 40,000 square feet.
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