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 the length of the rectangle be l and the breadth be b.
The perimeter of the rectangle is given by 2(l+b).

According to the question, the ratio between the perimeter and the breadth is 3:1:

b
2(l+b)
​
=
1
3
​

2l+2b=3b
2l=b
Given that the area of the rectangle is 310 sq. cm:

Area=l×b=310
Substitute b=2l into the area equation:

l×(2l)=310
2l
2
=310
l
2
=155
l=
155

​
≈12.449 cm
Thus, the length of the rectangle is nearly 12.45 cm.