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Question:

An isosceles triangle has perimeter 30cm and each of the equal sides is 12cm. Find the area of the triangle.

Solution:

Let the third side of the triangle be x⇒Perimeter=30 cm
semiperimeter(s)=perimeter/2⇒2S=30,S=15
Given:⇒12+12+x=30⇒x=6⇒A=√s(s−a)(s−b)(s−c) (Heron's formula)⇒A=√15(15-12)(15-12)(15-6)=√15(3)(3)(9)⇒A=9√15 cm2