Question

What is the circum radius for triangle sides $9cm,40cm$ and $41cm$.

• A. $9cm$
• B. $20.5cm$
• C. $21cm$
• D. None of these

Answer 1

The correct option is B $20.5cm$

If a, b, c are the sides of a triangle, then circum radius $=\frac{abc}{4Areaoftriangle}$

Sides of triangle are $9$cm, $40$cm, $41$cm

Area of triangle$=\sqrt{s(s-a)(s-b)(s-c)}$ where $s=\frac{a+b+c}{2}$

(Heron's formula)

$s=\frac{9+40+41}{2}=\frac{90}{2}=45$

Area of triangle$=\sqrt{45(45-9)(45-40)(45-41)}$

$=\sqrt{\mathrm{45.36.5.4}}$

$=2\times 5\times 3\times 6$

$=180$

Circum radius$=\frac{9\times 40\times 41}{4\times 180}=\frac{41}{2}=20.5$cm

$\therefore$ Circum radius$=20.5$cm.