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Example-10

The perimeter of an isosceles triangle is 32 cm. The ratio of the equal side to its
base is 3: 2. Find the area of the triangle.

Solution:

According to the question,

Perimeter of the isosceles triangle = 32 cm

It is also given that,

Ratio of equal side to base = 3: 2

Let the equal side = 3x

So, base = 2x

Perimeter of the triangle = 32 cm

⇒ 3x + 3x + 2x = 32

⇒ 8x = 32

⇒ x = 4.

Equal side = 3x = 3×4 = 12 cm

Base = 2x = 2×4 = 8 cm

The sides of the triangle = 12cm, 12cm and 8cm.

Let a = 12, b = 12, c = 8

S= + + = 12+12+8 = 16 cm.
2 2

Area of the triangle = − − −

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