Question

An isosceles triangle has perimeter $36cm$ and each of its equal sides is $13cm$ long . The area of the triangle is

Answer 1

$\begin{array}{c}Wehave\\ perimeteroftriangle=36cm\\ and,itstwoequalsides=13cm\\ Letthirdsidebexcm\\ Then\\ perimeter=36cm\\ 13+13+x=36\\ \therefore x=10cm\\ Now\\ Semi-perimeterS=\frac{perimeter}{2}\\ =\frac{36}{2}cm=18cm\\ Now\\ Areaoftriangle=\sqrt{s\left(s-a\right)\left(s-b\right)\left(s-c\right)}\\ =\sqrt{18\left(18-13\right)\left(18-13\right)\left(18-10\right)}c{m}^2\\ =\sqrt{18\left(5\right)\left(5\right)\left(8\right)}c{m}^2\\ =\sqrt{2\times 3\times 3\times 5\times 5\times 2\times 2\times 2}c{m}^2\\ =2\times 3\times 5\times 2c{m}^2\\ =60c{m}^2.\\ Hence,\\ Areaoftrinagle=60c{m}^2.\end{array}$