If the perimeter of a rectangle is 22 cm, then what will be its length and breadth?
Answers
=L=length
B-breadth
Perimeter = 2L+2B = L+L+B+B = 22
There is no single answer to this question, but an infinite number of possible answers within a range. In order to find that range, we have to figure out the limits of both B and L.
To find the limit, you can do some calculus, or simply solve for one variable as the other approaches zero. We know we can use zero as the limit, because at the point that one of the dimensions reaches zero, it stops being a rectangle and starts being a line. These are going to be interchangeable, as they are both variables, dependent on each other.
Perimeter = 22
22 = 2L+2B
Let L = 0
22 = 2(0) + 2B
22 = 2B
B = 11
Now we know that if L = 0, B = 11. But, when L = 0, it is no longer a rectangle. It simply becomes a line. So, we can say that as L approaches 0, B approaches 11, but we can’t ever actually get to 11. The inverse is true as well.
This can be states as:
B < 11
L < 11
You can also solve the above equation for one of the variables:
22 = 2L+2B
2L = 22 - 2B
L = (22 - 2B)/2
L = 11 - B
Your complete answer would be:
0 > L > 11;
0 > B > 11;
L = 11 - B.
You can check this answer by plugging in any number within the range, and solving for the perimeter, verifying that the answer is 22 units.
Let’s go with B=5:
L = 11 - B
Let B = 5
L = 11 - (5)
L = 6
Perimeter = L+L+B+B
Perimeter = 6+6+5+5 = 22
B = 11
This is the answer for the question