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 35 (Option 35).

Step-by-Step Explanation:

Step 1: Find the radius of the circle.

We are given that the area of the circle is 616 cm².

The formula for the area of a circle is:

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

Substituting the given value and taking $\pi =\frac{22}{7}$:

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

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

$r^2=28\times 7$

$r^2=196$

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

Step 2: Find the diameter of the circle (which is equal to the breadth of the rectangle).

The diameter of the circle is twice its radius:

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

According to the question, the breadth ($b$) of the rectangle is equal to the diameter of the circle:

$b=28\text{cm}$

Step 3: Find the length of the rectangle.

The ratio of the breadth to the length ($b:l$) of the rectangle is given as 4 : 5.

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

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

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

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

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

Thus, the length of the rectangle is 35 cm.