Question

the perimeter of an isosceles triangle is 32cm the ratio of the equal side to its base is 3:2 find the area of the triangle​

Answer 1

$\textbf{\underline{\underline{According\:to\:the\:Question}}}$  

Perimeter of isosceles triangle

= 32 cm

As we know that,

Perimeter of isosceles triangle

${\boxed{\bigstar{{2\times side\:which\:is\:equal+base}}}}$          

Now,

Assumption,

Length of equal side

= 3p

Also

Base = 2p

Then situation will be :-

2 × 3p + 2p = 32

6p + 2p = 32

8p = 32

p = 32/8

p = 4 cm

Length of side

= 3 × 4

= 12 cm

Length of base

= 2 × 4

= 8 cm

Area of isosceles triangle

$8\times\frac{1}{4}\sqrt{4\times 144-64}$

= 2√512

= 2 × 22.62

= 45.25 cm²

Answer 2

Answer:

45.24 cm²

Step-by-step explanation:

Let the side be a , b and c .

For isosceles we know two side are equal here a = b.

Given :

Perimeter = 32

a + a + c = 32

2 a + c = 32  ... ( i )

Also given ratio :

a / c = 3 / 2

2 a = 3 c

In ( i )

3 c + c = 32

c = 8

2 a = 3 c

2 a = 24

a = 12 cm

b = 12 cm

Using :

s = 32 / 2 = 16 cm

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

Area of triangle = √ 16 × 4 × 4 × 8

Area of triangle = 16 × 2.828 cm²

Area of triangle = 45.24 cm²