The breadth of a rectangle is equal to the diameter of a circle. The area of the circle is 616 cm². If the ratio of the breadth to the length of the rectangle is 4 : 5, then find the length of the rectangle (in cm).

The correct answer is Option 35.

Step 1: Find the radius of the circle.
The formula for the area of a circle is:

$\text{Area}=\pi r^2$

Given that the area of the circle is 616 cm² and taking $\pi =\frac{22}{7}$:

$616=\frac{22}{7}\times r^2$

$r^2=\frac{616\times 7}{22}$

$r^2=28\times 7=196$

$r=\sqrt{196}=14\text{cm}$

Step 2: Determine the breadth of the rectangle.
The diameter of the circle is twice its radius:

$\text{Diameter}=2\times r=2\times 14=28\text{cm}$

Since the breadth ($b$) of the rectangle equals the diameter of the circle:

$b=28\text{cm}$

Step 3: Calculate the length of the rectangle.
We are given that the ratio of breadth to length ($l$) is 4 : 5:

$\frac{b}{l}=\frac{4}{5}$

Substitute the value of breadth ($b=28$):

$\frac{28}{l}=\frac{4}{5}$

$l=\frac{28\times 5}{4}$

$l=7\times 5=35\text{cm}$

Therefore, the length of the rectangle is 35 cm.