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1. Length = 5 ft & width = 5 ft of a rectangle that has the given area .

                          

   What is called rectangle?

   • A Rectangle is a four sided-polygon, having all the internal angles equal to 90 degrees.
   • The two sides at each corner or vertex, meet at right angles.
   • The opposite sides of the rectangle are equal in length which makes it different from a square.

   Let the length and width of rectangle be x feet and y feet respectively.

   Give       area = 25 feet²

                   x y = 25 feet²

                    y = 25/x feet²   ………………1

   Now let perimeter is p

   then    p = 2 (x+y) = 2x + 2y

              p = 2x + 2 × 25/x

              P = 2X + 50/x

   diffrentiating w.r.t. x

               p’  = 2 – 50/x² ……………..2

   putting p’ = 0 to find critical point

           2 –  50/x²   = 0

             x²  = 25

              x  = 5                         [ x ≠ 5 ∴ length can not be negative ]

   Now,    p” = 0 + 100/ x³                       from (2)

   checking value of p” at critical point

         p” at x = 5        = 100/(x)³         > 0

   Hence, perimeter is minimum at x = 5 ft

   putting       x = 5  in equation 1

                     y = 1

   Hence,          length = 5 ft

                          width = 5 ft

   Learn more about rectangle

   brainly.com/question/20693059

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