Determine the maximized area of a rectangle that has a perimeter equal to 56m by creating and solving a quadratic equation. What is the length and width?

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

step-by-step explanation:

kjswgdkxg