Question

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.

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