The perimeter of an isosceles triangle is 64 cm and each of the equal sides is 5/6 times the base. What is the area (in cm2) of the triangle? ?->(Show Answer!)

1. The perimeter of an isosceles triangle is 64 cm and each of the equal sides is 5/6 times the base. What is the area (in cm2) of the triangle?

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By: anil on 05 May 2019 02.27 am

Let the length of base = $$6x$$ cm => Length of each equal side = $$frac{5}{6} imes6x=5x$$ cm => Perimeter = $$6x+5x+5x=16x=64$$ => $$x=frac{64}{16}=4$$ => Base = $$b=24$$ cm and side = $$a=20$$ cm Now, height of an isosceles triangle = $$h=sqrt{(a)^2-(frac{b}{2})^2}$$ => $$h=sqrt{(20)^2-(12)^2}$$ => $$h=sqrt{400-144}=sqrt{256}=16$$ cm $$ herefore$$ Area of isosceles triangle = $$frac{1}{2} imes(b) imes(h)$$ = $$frac{1}{2} imes24 imes16=192$$ $$cm^2$$ => Ans - (B)

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