Question

The perimeter of a triangle is $30cm$ and the circumference of its incircle is $88cm.$ The area of the triangle is

• A. $70c{m}^2$
• B. $140c{m}^2$
• C. $210c{m}^2$
• D. $420c{m}^2$

Answer 1

The correct option is C

$210c{m}^2$

Circumference of incircle $=88cm$
$\Rightarrow 2\pi r=88\Rightarrow r=\frac{88}{2\pi }=14cm$
Let the sides of the triangle be $a,b$ and $c$
Perimeter of $\Delta ABC$ $=a+b+c=30cm$

Area of $\Delta ABC=$ Area of $\Delta OBC+$ Area of $\Delta OCA+$ Area of $\Delta OAB$
$=\frac{1}{2}BC.OD+\frac{1}{2}AC.OE+\frac{1}{2}AB.OF=\frac{1}{2}a\times 14+\frac{1}{2}\times b\times 14+\frac{1}{2}\times c\times 14=\frac{1}{2}\times 14(a+b+c)=7\times 30=210c{m}^2$