The perimeter of an isosceles triangle is 32cm. The ratio of one of the equal side to its base is 3: 2. Find the area of the triangle.
It is given in the question that,
Perimeter of an isosceles triangle = 32 cm
Let us assume the sides of the triangle be a, b, c and a = b
We know that,
Perimeter = a + b + c
32 = a + b + c
32 = a + a + c
32 = 2a + c (i)
According to the condition given in the question, we have:
a: c = 3: 2
So, a = 3x and c = 2x
Now putting values of a and c in (i), we get
2 × 3x + 2x = 32
6x + 2x = 32
8x = 32
x =
x = 4
Thus, a = 3 × 4 = 12 cm
b = 12 cm
c = 2 × 4 = 8 cm
Now, s =
=
= 16 cm
Area of triangle =
=
=
= 4 × 4 × 2
= 32 cm2