The sides of a triangle are in the ratio 3:5:6. If its perimeter is 56 cm, use the Heroes formula to find its area

First, let's find the lengths of the sides of the triangle. If the sides are in the ratio 3:5:6, then we can say the sides are 3x, 5x, and 6x. The perimeter of the triangle is the sum of its sides, so:

3x + 5x + 6x = 56 14x = 56 x = 56 / 14 x = 4

So, the sides of the triangle are 34 = 12 cm, 54 = 20 cm, and 6*4 = 24 cm.

Next, let's use Heron's formula to find the area of the triangle. Heron's formula is √[s(s - a)(s - b)(s - c)], where s is the semi-perimeter of the triangle, and a, b, and c are the sides of the triangle.

First, let's find s:

s = (a + b + c) / 2 s = (12 + 20 + 24) / 2 s = 56 / 2 s = 28

Now, let's substitute s, a, b, and c into Heron's formula:

Area = √[s(s - a)(s - b)(s - c)] Area = √[28(28 - 12)(28 - 20)(28 - 24)] Area = √[28168*4] Area = √[11264] Area = 106.06601717798213 cm²

So, the area of the triangle is approximately 106.07 cm².