Question

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

Answer 1

Given :-

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

To Find :-

Area

Solution :-

Let the sides be 3a and 2a

3a + 3a + 2a = 32

8a = 32

a = 32/8

a = 4

Sides are

3a = 3(4) = 12 cm

3a = 3(4) = 12 cm

2a = 2(4) = 8 cm

Now

Semiperimeter = a + b + c/2

Semiperimeter = 12 + 12 + 8/2

Semiperimeter = 32/2

Semiperimeter = 16 cm

Area = √s(s - a)(s - b)(s - c)

Area = √16(16 - 12)(16 - 12)(16 - 8)

Area = √16 × 4 × 4 × 8

Area = √2048

Area = 32√2 cm²

Answer 2

Answer :

• Area of the triangle is 32√2 cm²

Given :

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

To find :

• Area of the triangle

Solution :

Given, the ratio of the equal side to its base is 3:2 so,

• Let the equal sides and base be 3x and 2x

• Other side be 3x

Given, Perimeter is 32cm so,

➟ 3x + 3x + 2x = 32

➟ 8x = 32

➟ x = 32/8

➟ x = 4cm

• Equal side = 3x = 3(4) = 12cm
• Base = 2x = 2(4) = 8cm

Then,

• Sides of triangle are 12cm , 12cm and 8cm

We know that Semi perimeter of triangle :

• s = a + b + c / 2

Where,

• a is 12cm
• b is 12cm
• c is 8cm

➟ s = a + b + c / 2

➟ s = 12 + 12 + 8 / 2

➟ s = 32/2

➟ s = 16

Finding the area of the triangle :

We know that

• Area of the triangle = √s(s - a) (s - b) (s - c)

Where ,

• s is semi perimeter of triangle
• a,b,c is sides of triangle

➟ Area of the triangle = √s(s - a) (s - b) (s - c)

➟ Area of the triangle = √16(16 - 12) (16 - 12) (16 - 8)

➟ Area of the triangle = √16 × 4 × 4 × 8

➟ Area of the triangle = √2048

➟ Area of the triangle = 32√2 cm²

Hence, Area of the triangle is 32√2 cm²