# Find the dimensions of a rectangle with perimeter 100 m whose area is as large as possible.

Area is defined as total space occupied by a surface and perimeter is defined as total length of rectangle.

## Answer: The dimensions of a rectangle with perimeter 100 m whose area is as large as possible dimension is 25m and** **25m

Area of rectangle is defined as **length x breadth** and Perimeter of rectangle is defined as **2 times sum of length and breadth**

**Explanation:**

Let 'A' be area and 'P' be perimeter of the rectangle

Let 'x' be the width and 'y' be the length

We know that,

**Perimeter = 2 (length + breadth)**

Hence,

P = 2(x+y)

=> 100 = 2(x+y) (Since, Perimeter = 100m)

=> x + y = 50

=> y = 50 - x ----------------------------- (1)

We know that,

**Area of a rectangle = Length × Breadth**

Hence,

A = xy

By substituting the value of y from equation (1) to equation (2) we get,

A(x) = x(50 - x )

A(x) = 50 x - x^{2}

Computing the derivative of A(x) we get,

A'(x) = 50 - 2x

Finding the critical points,

50 - 2x = 0

=> 2 x = 50

=> x = 25

Substitute x = 25 in equation (1)

We get,

y = 50 - x

=> y = 25