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The perimeter of an isosceles triangles is 42 cm and its base is 1 1/2 t...

The perimeter of an isosceles triangles is 42 cm and its base is 1 1/2 times each of the equal of the equal sides. Find (i) the length of each side of the triangle (ii) the area of the triangle, and (iii) hte height of the triangle

Ok

Let The Equal Sides Be x cm.

Now

Base = 3/2*x = 3x/2

Perimeter = Sum Of All The Sides

3x/2+x+x = 42

7x/2 = 42

7x = 84

x = 12

Now Base = 3/2*12 = 18

So Sides Are 18,12 And 12 cm.

Here All The Three Sides Are Given So We Find Out Area Through Herons Formula

Here S = 18+12+12/2 = 21cm

Apply Formula

Area = Square Root (21*(21-18)*(21-12)*(21-12) )

=> Square Root (21*3*9*9)

=> Square Root (5103)

=> 71.435

Now Area Of Triangle = 1/2*Base*Height

Base = 18cm

9*Height = 71.435

Height = 7.9 (Approximately)