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  • The perimeter of an isosceles triangle is 42 cm and its base is (3/2) times each of the equal sides. Find the length of each side of the triangle, area of the triangle and the height of the triangle.

The perimeter of an isosceles triangle is 42 cm and its base is (3/2) times each of the equal sides. Find the length of each side of the triangle, area of the triangle and the height of the triangle.

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eginarrayl extLet two equal sides AB and AC be x.\ Base BC=frac32x\ extPerimeter=42\ x+x+frac3x2=42\ Rightarrow frac7x2=42\ Rightarrow x=12\ AB=AC=12\ \ In riangle ADC\ AC^2=AD^2+DC^2\ 12^2=AD^2+9^2\ 144-81=AD^2 \ AD^2=63\ AD=sqrt63=3sqrt7\ extHeight of triangle=AD=3sqrt7 \ \ extHence\ Area =frac12 imes baseleft(AD ight) imes heightleft(BC ight)\ =frac12 imes18 imes3sqrt7=27sqrt7endarrayeginarrayl\ endarray

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Deependra Verma

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