Listen NCERT Audio Books to boost your productivity and retention power by 2X.
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