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

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GIVEN

3/2 x +x +x=42cm

3x/2 + 2x =42

(3x+4x)/2=42

3x+4x=84

7x=84

x=12cm

side=12cm base=18cm

The height(altitude) of an isos. trangle divides it into two rt trangles

in a rt.trangle, base²+heigrt²=hypotenuse²

thus, 9²+h²=12²

h=√12²-9²

=√144-81 =√63 =3√7cm

area =1/2 x base x hieght

=1/2 x 18 x3√7

27√7cm²