3 Tutor System
Starting just at 265/hour

# An isosceles triangle has perimeter 30 cm arid each of the equal sides is 12 cm. Find the area of the triangle.

Let $$\triangle{ABC}$$ be an isosceles triangle, in which,

We have,
AB = AC = 12cm ...(Given)

Now, AB + AC + BC = 30
(Given, perimeter = 30cm)

$$\Rightarrow$$ 12 + 12 + BC = 30
$$\Rightarrow$$ BC = 30 - 24
$$\Rightarrow$$ BC = 6cm

Now, we know that,
$$s = \frac{a + b + c}{2}$$
$$\therefore$$ $$s = \frac{30}{2} = 15cm$$

Now, Area of triangle
= $$\sqrt{15(15 - 12)(15 - 6)(15 - 12)}$$
(Since, Heron's formula [area = $$\sqrt{s(s - a)(s - b)(s - c)}$$])

= $$\sqrt{15 × 3 × 9 × 3}$$
= $$\sqrt{3 × 5 × 9 × 9}$$
= $$9\sqrt{15} {cm}^2$$