Question

The perimeter of a triangle is 30 cm 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 = 88 cm
$\Rightarrow 2\pi r=88\Rightarrow r=\frac{88}{2\pi }=14cm$

Perimeter of $\Delta ABC$ = a + b + c = 30 cm

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