Question

The perimeter of an isosceles triangle is 42 cm in subhasis two by three times the sum of the equal sides find the length of each side and the area 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