Find the length and width (in feet) of a rectangle that has the given area and a minimum perimeter. Area: 25 square feet
Length = 5 ft & width = 5 ft of a rectangle that has the given area .What is called rectangle?
Let the length and width of rectangle be x feet and y feet respectively.Give area = 25 feet²x y = 25 feet²y = 25/x feet² ………………1Now let perimeter is pthen p = 2 (x+y) = 2x + 2yp = 2x + 2 × 25/xP = 2X + 50/xdiffrentiating w.r.t. xp’ = 2 – 50/x² ……………..2putting p’ = 0 to find critical point2 – 50/x² = 0x² = 25x = 5 [ x ≠ 5 ∴ length can not be negative ]Now, p” = 0 + 100/ x³ from (2)checking value of p” at critical pointp” at x = 5 = 100/(x)³ > 0Hence, perimeter is minimum at x = 5 ftputting x = 5 in equation 1y = 1Hence, length = 5 ftwidth = 5 ftLearn more about rectanglebrainly.com/question/20693059#SPJ4
- 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.