We know that the lateral sides of an isosceles triangle are of equal length
Consider the length of lateral side as x cm
It is given that base = 3/2 × x cm
(i) It is given that the perimeter = 42cm
We can write it as
x + x + 3/2 x = 42cm
By multiplying the entire equation by 2
2x + 2x + 3x = 84cm
On further calculation
7x = 84
By division
x = 12 cm
So the length of lateral side = 12 cm
Base = 3/2 x = 3/2 (12)
So we get the base = 18cm
Therefore, the length of each side of the triangle is 12cm, 12 cm and 18cm.
(ii) Consider a = 12cm, b = 12cm and c = 18cm
Therefore, the area of the triangle is 71.28cm2.
(iii) We know that
Area of a triangle = ½ × b × h
By substituting the values
71.28 = ½ × 18 × h
On further calculation
71.28 = 9 × h
By division
h = 7.92 cm
Therefore, the height of the triangle is 7.92 cm.
