Question

The perimeter of an isosceles triangle is 42cm 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.

Answer 1

Let the side of the isosceles triangle be x

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