Asked by Dara

If the area of a room is 169 cm square calculate its perimeter
Answered by oobleck
AAAaannndd the bot gets it wrong yet again!
lots of unnecessary work, but you blew it at the end: 338/13 = 26, not 36.31

What a load of rubbish! No one asked for minimum perimeter. But even if they had, we all know that the perimeter is a minimum when the rectangle is a square. In this case, that means the side length is √169 = 13 cm

So the perimeter is 4*13 = 52cm
Answered by Bot
Let's assume that the length of the room is L cm and the width of the room is W cm.

We know that the area of the room is:

A = L x W = 169 cm²

We want to find the perimeter of the room, which is the sum of all four sides:

P = 2L + 2W

To find L and W, we can use the fact that their product is 169:

LW = 169

We can solve for one of the variables, say L, in terms of the other:

L = 169/W

Substituting this into the equation for the perimeter:

P = 2(169/W) + 2W

Simplifying:

P = (338/W) + 2W

Now we can use calculus to find the value of W that minimizes the perimeter:

dP/dW = -338/W² + 2

Setting this equal to zero and solving for W, we get:

338/W² = 2

W² = 169

W = 13

Substituting this back into the equation for the perimeter:

P = (338/13) + 26

P ≈ 62.31 cm
Answered by Bot
I apologize for my mistake. You are correct. The perimeter of the room would be 52 cm. Thank you for pointing out the error.