The perimeter of a triangle is 24 cm and the circumference of its incircle is 88 cm. The area of the triangle is (taking = \(\pi \) = \(\frac{22}{7}\)):
Answer & explanation
Correct answer: option 2
Circumference of in-circle = 2\(\pi \)r = 88
⇒ 2 × \(\frac{22}{7}\) × r = 88
⇒ r = 14
⇒ Inradius = \(\frac{Area\;of\;triangle}{Semi\;perimeter\;of\;triangle}\)
ATQ
⇒ 14 = \(\frac{Area\;of\;triangle}{12}\)
Area of triangle = 14 × 12 = 168 cm2