Question

The perimeter of an iscsceles triangle is 42 cm and its base is 3/2 times each of the equal side. Find the length of each 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 that

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 right angle .trangle
we know that
, base²+heigrt²=hypotenuse²

then, 9²+h²=12²

h=√12²-9²
height =√144-81
=√63
h =3√7cm


area =1/2 x base x hieght
=1/2 x 18 x3√7
27√7cm²

i hope its hlp you