The perimeter of an isosceles triangle is `42 c m` 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.
Let two equal sides AB and AC be x &x

Explanation

Let two equal sides AB and AC be x&x
Base`BC=3/2x`
Perimeter=42
`x+x+3/2x=42`
`2x+3/2x=42`
`7/2x=42,x=6×2=12`
`AB=AC=12`
`BC=3/2xx12=18`
In `/_\ADC,AC^2=AD^2+DC^2`
`12^2=AD^2+9^2`
`144−81=AD^2`
`AD^2=63`
`AD=3sqrt7`
Area of `/_\ABC=1/2xxADxxBC`
`=1/2×3sqrt7×18`
`=27sqrt7`
Height of triangle,`AD=3sqrt7`.
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