The ratio between the perimeter and the breadth of a rectangle is 5 : 1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle?

To find the length of the rectangle, we need to use the given information about the ratio between the perimeter and the breadth, as well as the area of the rectangle.

Let's assume that the breadth of the rectangle is x cm.

According to the given ratio, the perimeter of the rectangle is 5 times the breadth. So, the perimeter would be 5x cm.

The formula for the perimeter of a rectangle is P = 2(length + breadth). Since the breadth is x cm, we can write the equation as 5x = 2(length + x).

Now, let's use the area of the rectangle to solve for the length. The formula for the area of a rectangle is A = length * breadth. We are given that the area is 216 sq. cm, so we can write the equation as 216 = length * x.

Now we have two equations:

1. 5x = 2(length + x)
2. 216 = length * x

To solve these equations, we can substitute the value of length from equation 2) into equation 1).

Substituting length * x for 216 in equation 1), we get: 5x = 2(length + x) 5x = 2(216/x + x)

Simplifying this equation, we get: 5x = 432/x + 2x

Multiplying both sides by x, we get: 5x^2 = 432 + 2x^2

Bringing all terms to one side, we get: 3x^2 = 432

Dividing both sides by 3, we get: x^2 = 144

Taking the square root of both sides, we get: x = 12

So, the breadth of the rectangle is 12 cm.

Now, we can substitute this value of x into equation 2) to find the length: 216 = length * 12

Dividing both sides by 12, we get: length = 216/12 length = 18

Therefore, the length of the rectangle is 18 cm.