Ask a Teacher

Search



The area of the incircle of an equilateral triangle is 154 square centimeter.What is the perimeter of the triangle? (Use ?3= 1.73)
ABC an equilateral triangle
? AB = BC = AC ......... (1)
 
Let r be the radius of inscribed circle of centre O.
 
Given: Area of circle = 154 cm2
? ?r 2 = 154 cm2

Draw OD ? AB and OE ? AC.
? OD = OE = r (radius)
 
In ? ODA = ? OED,
? ODA = ? OED [ Each of 90°, by construction ]
OD = OE [ Radius of circle ]
OA = OA [ Common ]
? By RHS congruence rule,
? ODA ? ? OED
? ? OAD = ? OAE [CPCT ]
 
Now ? BAC = ? DAE = 60° [ ? ABC is an equilateral triangle]
?? OAD + ? OAE = 60°
? 2? OAD = 60°
? ? OAD = 30°

In ? OAD


? ODA ? ? ODB
? AD = BD [CPCT]
 
Also, AB = AD + BD
= 2 AD



?Perimeter