Question

If circumference of circle is $51.04$ cm then what is the perimeter of a triangle whose three different sides are less than the radius of the given circle by $2$ cm, $3$ cm and $5$ cm respectively ? $(\pi =\frac{22}{7})$

• A. $38.72$ cm
• B. $14.36$ cm
• C. $38$ cm
• D. $48.72$ cm

Answer 1

The correct option is B $14.36$ cm

In order to find out the perimeter we must know the sides of triangles and sides are related to radius so let us find out the radius of circle first.
Let the radius be $r$ cm.
We know,
$\text{circumference}=2\pi r$
$51.04=2\times \frac{22}{7}\times r$
$r=\frac{51.04}{44}\times 7$
$r=7\times 1.16$
$r=8.12$ cm

So, sides of triangle are
$r-2=8.12-2=6.12$ cm
$r-3=8.12-3=5.12$ cm
$r-5=8.12-5=3.12$ cm

Now,
$\text{perimeter}=\left(\text{sum of all sides}\right)$
$\text{perimeter}=6.12+5.12+3.12$
$\text{perimeter}=14.36$ cm

Hence, option $\left(b\right)$ correct.