The area of a circle inscribed in an equilateral triangle is 154cm². Find the perimeter of the triangle.(Use π=22/7 and √3=1.73)
Answers
Step-by-step explanation:
Sol: Given area of inscribed circle = 154 sq cm Let the radius of the incircle be r. ⇒ Area of this circle = πr2 = 154 (22/7) × r2 = 154 ⇒ r2 = 154 × (7/22) = 49 ∴ r = 7 cm Recall that incentre of a circle is the point of intersection of the angular bisectors. Given ABC is an equilateral triangle and AD = h be the altitude. Hence these bisectors are also the altitudes and medians whose point of intersection divides the medians in the ratio 2 : 1 ∠ADB = 90° and OD = (1/3) AD That is r = (h/3) Þ h = 3r = 3 × 7 = 21 cm Let each side of the triangle be a, then Altitude of an equilateral triangle is (√3/2) times its side That is h = (√3a/2) ∴ a = 14√3 cm We know that perimeter of an equilateral triangle = 3a = 3 × 14 √3 = 42√3 = 42 × 1.73 = 72.66 cm l
