Question

the semi perimeter of an isosceles triangle is 21 cm and its base is 3/2

Answer 1

Let the three sides be x , y , z.

Semi perimeter is (x+y+z)/2 = 21 implies x + y + z = 42

Let x be the base implies x= 3/2 ~ 1.5

So, y + z = 42 - 1.5 = 40.5

Case(i): If x is one of the equal sides of isosceles triangles then y or z = 1.5 implies z or y = 40.5 - 1.5 = 39

i.e (x,y,z) = (1.5,1.5,39) or (1.5,39,1.5) ...........1

Case(ii) If x is not the equal side then y=z= 40.5/2 ~ 20.25

i.e (x,y,z) = (1.5,20.25,20.25) .........................2

Here 1 does not follow property of triangles - sum of any two sides must be greater than third side i.e  1.5+1.5 is not greater than 39

So the sides of triangle are 1.5 unit, 20.25 unit and 20.25 unit

(Also in general 'base' indicates unequal side of triangle)