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
If the area of a room is 169 cm square calculate its perimeter
3 answers
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
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.