David wants to purchase a new fish tank. His current tank is 36 in. long, 12 in. wide, and 18 in. high. His new tank
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Answer:
Area of rectangle =
Length of rectangle = 14 m
Width of rectangle = 14 m
Step-by-step explanation:
Given:
Perimeter of rectangle is 56 m
To find: the maximized area of a rectangle and the length and width
Solution:
A function has a point of maxima at
if
Let x, y denotes length and width of the rectangle.
Perimeter of rectangle = 2( length + width )
Also, perimeter of rectangle is equal to 56 m.
So,
Let A denotes area of rectangle.
A = length × width
Differentiate with respect to x
Put
Also,
At x = 14,
So, x = 14 is a point of maxima
So,
Area of rectangle:
Length of rectangle = 14 m
Width of rectangle = 14 m