If the area of a room is 169 cm square calculate its perimeter
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
I apologize for my mistake. You are correct. The perimeter of the room would be 52 cm. Thank you for pointing out the error.
To calculate the perimeter of the room, we first need to find the length of each side. Since the area of the room is given, we can find the length of one side by taking the square root of the area.
The area of the room is given as 169 cm². Taking the square root of 169, we find:
√169 = 13 cm
Since the room is square-shaped, all four sides are equal in length. Therefore, the length of each side is 13 cm.
To calculate the perimeter, we multiply the length of one side by 4, as there are four sides in a square.
Perimeter = 4 * 13 cm = 52 cm
Therefore, the perimeter of the room is 52 cm.
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