Question

The circumference of the circle in which 3multiply 4 rectangle is in scribed is

Answer 1

Answer:

Circumference of circle is $\frac{110}{7}$

Step-by-step explanation:

Rectangle inscribed in a circle must have its diagonal as diameter of circle.

Now, dimensions of rectangle are $3 \times 4$

Diagonal of rectangle is calculated as

$Diagonal = \sqrt{(\,3)\,^2 + (\,4)\,^2}\\\\ Diagonal = \sqrt{9 + 16}\\\\ Diagonal = \sqrt{25}\\\\ Diagona = \pm 5$

Also, diagonal can never be negative

Hence, diagonal of rectangle = 5

Now, Diameter of circle = Diagonal of rectangle = 5

Radius of circle = $\frac{5}{2}$

Circumference of circle is calculate as

$C = 2 \times \pi \times \frac{5}{2}\\\\ C = 2 \times \frac{22}{7} \times \frac{5}{2}\\\\ C = \frac{22 \times 5}{7}\\\\ C = \frac{110}{7}$