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

We know that,

In any isosceles triangle, the lateral sides are of equal length

Let,

The lateral side of the triangle be x

Given,

Base of the triangle = (i) We have to find out length of each side of the triangle:

Perimeter of the triangle = 42 cm (Given)

x + x + = 42 cm

2x + 2x + 3x = 84 cm

7x = 84 cm

x = x = 12 cm

Therefore,

Length of lateral side of the triangle = x = 12 cm

Base = = = 18 cm

Hence,

Length of each side of the triangle is 12 cm, 12 cm and 18 cm

(ii) Now, we have to find out area of the triangle:

Let,

a = 12 cm

b = 12 cm

And,

c= 18 cm

Now,

s = = = = 21 cm

We know that,

Area of triangle = = = = = 27 = 71.42 cm2

Therefore, area of the given triangle is 71.42 cm2

(iii) We have to calculate height of the triangle:

We know that,

Area of triangle = 71.42 cm2 = 71.42 cm2 = 9 × h

h = = 7.94 cm

Therefore, height of the triangle is 7.94 cm

11