-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?

Sure, let's solve this step by step.

Step 1: We know that the ratio of the perimeter (P) to the breadth (b) of the rectangle is 5:1. So, we can write this as P/b = 5/1.

Step 2: The formula for the perimeter of a rectangle is P = 2(l+b), where l is the length of the rectangle. Substituting this into our ratio, we get 2(l+b)/b = 5/1.

Step 3: Simplifying this equation, we get 2l/b + 2 = 5. Subtracting 2 from both sides, we get 2l/b = 3. So, the ratio of the length to the breadth is 3:2.

Step 4: We also know that the area (A) of the rectangle is 216 sq. cm. The formula for the area of a rectangle is A = lb. Substituting the values we know, we get 216 = lb.

Step 5: From step 3, we know that l/b = 3/2. So, we can substitute l = 3/2b into our area formula to get 216 = (3/2b)*b.

Step 6: Simplifying this equation, we get 216 = 3/2*b^2. Solving for b^2, we get b^2 = 216 * 2/3 = 144. So, b = sqrt(144) = 12 cm.

Step 7: Substituting b = 12 cm into our length formula from step 3, we get l = 3/2*12 = 18 cm.

So, the length of the rectangle is 18 cm.