Question

the base of an isosceles triangle is 24cm and it's area is 192sq.cm. find its perimeter ​

Answer 1

Answer:

64 cm

Step-by-step explanation:

64

Answer 2

Answer:

Perimeter of isosceles triangle is 81.68 cm .

Step-by-step explanation:

Given -

The base of an isosceles triangle is 24cm

Area of an isosceles triangle is 192sq.cm

To find -

Perimeter of isosceles triangle

Solution -

As we know that ,

Area of an isosceles triangle  = $\frac{bh }{2}$

Where ,

b = Base length

$h$ = height from top to base

put the given values in these formula

$192 =\frac{24 \times h }{2}$

$192 \times \frac{2}{24} =h$

Divide 192 by 24 we get

$8 \times 2 = h$

$h = 16$ cm

As in isosceles triangle height and base makes the right angle .

So, to find the side of triangle (a) we use Pythagoras theorem.

By applying Pythagoras theorem

$a^{2}= h^{2}+b^{2}$

$a^{2}= 16^{2}+24^{2}$

$a^{2}= 832$

$a=\sqrt{832}$

$a= 28.84$ cm

As we know that,

Perimeter of isosceles triangle = $2a+b$

Perimeter of isosceles triangle = $2\times28.84 + 24$

Perimeter of isosceles triangle = $57.68 +24$

Perimeter of isosceles triangle = $81.68$ cm

∴ Perimeter of isosceles triangle is 81.68 cm