Question

The equal sides of the isosceles triangle are 12 cm, and the perimeter is 30 cm. The area of this triangle is:

Answer 1

Step-by-step explanation:

Let the third side be the c.

Perimeter= sum of all side

30=12+12+c

C=30-24

=6 cm

By Herons formula

S=(12+12+6)/2

=15

Area=

$\sqrt{(15 - 12)(15 - 12)(15 - 6)15}$

=

$\sqrt{15 \times 3 \times 3 \times 9}$

$3 \sqrt{15 \times 9}$

$3 \sqrt{3 \times 5 \times 3 \times 3}$

$3 \times 3 \sqrt{15}$

$9 \sqrt{15}$

Answer 2

First,let the third side be x.

It is given that the length of the equal sides us 12 cm and it's perimeter is 30 cm.

So,$30=12+12+x$

$⇒ 30 = 24 + x$

$⇒24 + x = 30$

$⇒ x= 30 - 24$

$⇒ x = 6$

So,the length of the third side is 6 cm.

Thus,the semi perimeter of the isosceles triangle (s) = 30/2 cm =15 cm

By using Heron's Formula,

Area of the triangle,

$= \sqrt{s(s - a)(s - b)(s - c)}$

$= \sqrt{15(15 - 12)(15 - 12)(15 - 6)} \: {cm}^{2}$

$= \sqrt{15 \times 3 \times 3 \times 9} \: {cm}^{2}$

$= 9 \sqrt{15} \: {cm}^{2}$