The perimeter of an isosceles triangle is 392 and the base is 192. Find the area of the triangle.

The perimeter of an isosceles triangle is 392 cm. The base is 92 cm.

Let’s find the area of the triangle.

P = a + b + c = a + 2 * b;

b = (P – a) / 2 = (392 – 192) / 2 = 100 cm – the length of the side of the triangle.

We lower the height to the base, it will also be the median – a right-angled triangle is formed, one leg of which is half the base, the second is the height, the hypotenuse is the side of the triangle.

Then h ^ 2 = 100 ^ 2 – (192/2) ^ 2;

h ^ 2 = 10000 – 9216;

h = 28.

S = 1/2 h * a = 1/2 * 28 * 192 = 14 * 192 = 2688 cm².