Question

Find the minimum perimeter of a rectangle whose area is 169

Answer 1

Answer:

Let length =x , breadth  = y

xy = 169

y=169/x

Perimeter = 2(x+y) = 2x+338/x

Differentiate and equate it to zero to get minimum value

2-338/x^2 = 0

2x^2=338

x^2=169

x=13

y=13

Minimum perimeter = 2x+2y= 26+26 = 52

Step-by-step explanation:

Answer 2

Given,

The rectangle's area =  169cm²

To Find,

The rectangle's perimeter.

Solution,

Given that,

The area of the rectangle = 169cm²

To find rectangle's area  = length * breadth.

Let's take

Rectangle's length = lcm

Rectangle's width  = wcm

Then the area = l × w

Area l × w = 169cm²

l = 169/w

To find rectangle's perimeter

P = 2(l + w )

P = 2((169/w) + w)

338/w + 2w = P

Equate this to 0

2- 338/w²=0

2w² = 338

w² = 338/2

w²=169

w = √169

w = 13cm

to find length l

l*w = 169

l = 169/13

l = 13cm

Therefore,

the perimeter = 2(l+w)

P = 2(13+13)

P =2 * 26

P = 52cm.

Hence, 52cm is the perimeter of the rectangle whose area is 169cm².