Question

15. The perimeter of a triangular field is 144m and its sides are in the ratio 3:4:5. Find the length of the
perpendicular from the opposite vertex to the side whose length is 60m.​

Answer 1

Answer:

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Answer 2

Given,

Perimeter of the triangular field = 144m

Ratio of the sides = 3:4:5

To find,

The length of the perpendicular from the opposite vertex to the side whose length is 60m.

Solution,

We can simply solve this mathematical problem by using the following mathematical process.

Let, the length of the three sides of the triangular field = 3x metres , 4x metres and 5x metres

Perimeter of the triangular field = (3x+4x+5x) = 12x metres

According to the data mentioned in the question,

12x = 144

x = 12

Length of the sides :

First side = 3×12 = 36 m

Second side = 4×12 = 48 m

Third side = 5×12 = 60 m

Semi-perimeter of the triangular field = 144/2 = 72 m

Now,

Area of the triangle = √72×(72-36)×(72-48)×(72-60) = √(72×36×24×12) = √746496 = 864 m²

Now,

Assuming,

Height (perpendicular from the opposite vertex to the side) = h metres

Base = 60 metres (As, the perpendicular should dropped on the 60m side.)

Area = ½ × 60 × h = 30h m²

Thus,

30h = 864

h = 28.8 m

Hence, the length of the perpendicular will be 28.8 metres.