Question

The perimeter of a triangular field is 240 dm. If two of its sides are 78 dm and 50 dm, find
the length of the perpendicular on the side of length 50 dm from the opposite vertex.

Please tell me the answer fast..​

Answer 1

Given data : The perimeter of a triangular field is 240 dm. If two of its sides are 78 dm and 50 dm.

To find : The length of the perpendicular on the side of length 50 dm from the opposite vertex.

Solution : Here, according to given,

⟹ perimeter of a triangular field = 240 dm

⟹ two sides of a triangular field = 78 dm and 50 dm

Let, first side of triangle be a, second side be b, and third side be c.

Where,

⟹ a = 78 dm

⟹ b = 50 dm {acco. to given, base of triangular field}

⟹ c = ?

Now, by formula of perimeter :

⟹ perimeter of triangle = a + b + c

⟹ 240 = 78 + 50 + c

⟹ 240 = 128 + c

⟹ c = 240 - 128

⟹ c = 112 dm

{Here, we use Heron's formula}

Now, s = semi perimeter

⟹ s = (a + b + c)/2

⟹ s = (78 + 50 + 112)/2

⟹ s = (128 + 112)/2

⟹ s = 240/2

⟹ s = 120 dm

⟹ Area = √{s * (s - a) * (s - b) * (s - c)}

⟹ Area = √{120 * (120 - 78) * (120 - 50) * (120 - 112)}

⟹ Area = √{120 * 42 * 70 * 8}

⟹ Area = √{5040 * 70 * 8}

⟹ Area = √{352800 * 8}

⟹ Area = √2822400

⟹ Area = 1680 dm²

Let, the length of the perpendicular on the side of length 50 dm from the opposite vertex be the height of triangular field.

⟹ Area = ½ * base * height

⟹ 1680 = ½ * 50 * height

⟹ 1680 = 25 * height

⟹ height = 1680/25

⟹ height = 67.2 dm

Answer : Hence, height of triangular field is 67.2 dm. {or the length of the perpendicular on the side of length 50 dm from the opposite vertex is 67.2 dm}