Find the area of the triangle whose sides are 42 cm, 34 cm and 20 cm in length. Hence, findthe height corresponding to the longest side

To find the area of the triangle, we can use Heron's formula.

Step 1: Calculate the semi-perimeter (s) of the triangle using the formula: s = (a + b + c) / 2, where a, b, and c are the lengths of the sides of the triangle. In this case, a = 42 cm, b = 34 cm, and c = 20 cm. So, s = (42 + 34 + 20) / 2 = 96 / 2 = 48 cm.

Step 2: Use Heron's formula to find the area (A) of the triangle: A = √(s(s-a)(s-b)(s-c)) Substituting the values, we get: A = √(48(48-42)(48-34)(48-20)) A = √(48(6)(14)(28)) A = √(48 * 6 * 14 * 28) A = √(56448) A ≈ 237.68 cm² (rounded to two decimal places).

Now, to find the height corresponding to the longest side, we can use the formula for the area of a triangle: A = (base * height) / 2.

Step 3: Rearrange the formula to solve for the height (h): h = (2 * A) / base.

Since the longest side is 42 cm, the base of the triangle is 42 cm. Substituting the values, we get: h = (2 * 237.68) / 42 h = 475.36 / 42 h ≈ 11.32 cm (rounded to two decimal places).

Therefore, the area of the triangle is approximately 237.68 cm² and the height corresponding to the longest side is approximately 11.32 cm.