Question

perimeter of isosceles triangle is 30 cm and its equal side 12 cm each find the area of a triangle​

Answer 1

Answer:

$\boxed{\bold{9 \sqrt{15} \: cm^2}}$

Step-by-step explanation:

Let the unequal side of the triangle be a. Then, a = 30 - 2(12) = 30 - 24 = 6 cm.

Semiperimeter (s) = 30/2 = 15 cm

Thus, area of triangle by Heron's formula

$= \sqrt{15(15-12)(15-12)(15-6)}\\\\= \sqrt{3 \times 5 \times 3 \times 3 \times 3 \times 3}\\\\= 3 \times 3 \times \sqrt{15}\\\\= \boxed{\bold{9 \sqrt{15} \: cm^2}}$

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,

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

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

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

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