The ratio between the perimeter and the breadth of a rectangle is 3 : 1. If the area of the rectangle is 310 sq. cm, the length of the rectangle is nearly:

Let's solve this step by step:

Step 1: Let's denote the breadth of the rectangle as b and the length as l. According to the problem, the ratio between the perimeter and the breadth of the rectangle is 3:1. The formula for the perimeter of a rectangle is 2*(l+b). So, we can write this ratio as 2*(l+b) : b = 3 : 1.

Step 2: Simplifying this ratio gives us l+b = 1.5b. From this, we can express the length l in terms of the breadth b as l = 1.5b - b = 0.5b.

Step 3: The problem also tells us that the area of the rectangle is 310 sq. cm. The formula for the area of a rectangle is l*b. Substituting the expression for l from step 2 into this formula gives us 0.5b * b = 310.

Step 4: Solving this equation for b gives us b^2 = 620. Taking the square root of both sides gives us b = sqrt(620) = 24.9 cm (approximately).

Step 5: Substituting b = 24.9 cm into the expression for l from step 2 gives us l = 0.5 * 24.9 = 12.45 cm (approximately).

So, the length of the rectangle is approximately 12.45 cm.