Question

Perimeter of a triangular ground is 900 m and it's side are in the ratio 3:4:5 using Heron,find the area of the ground

Answer 1

Step-by-step explanation:

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Answer 2

Given :

• Perimeter of Triangular Ground = 900 m
• sides of triangular ground are in the ratio 3 : 4 : 5

To find :

• Are of triangular ground Using Heron's Formula

Formula required :

• Heron's formula

    Ar (Δ) = √( s (s - a) (s - b) (s - c) )

[ where, s is semi-perimeter of triangle; a, b, c are three sides of triangle ]

Solution :

Given that sides of triangle are in the ratio 3 : 4 : 5

so, Let three sides of triangle be

• a = 3 x
• b = 4 x
• c = 5 x

now, since perimeter of triangle is 900 m

therefore,

→ a + b + c = 900

→ 3 x + 4 x + 5 x = 900

→ 12 x = 900

→ x = 75

so, three sides of triangle would be

• a = 3 (75) = 225 m
• b = 4 (75) = 300 m
• c = 5 (75) = 375 m

now,

semi-perimeter of triangle will be

→ s = 900 / 2

→ s = 450 m

Using Heron's formula

→ Ar (Δ) = √( s (s - a) (s - b) (s - c) )

→ Ar (Δ) = √( 450 × (450 - 225) × (450 - 300) × (450 - 375) )

→ Ar (Δ) = √(450 × 225 × 150 × 75)

→ Ar (Δ) = 33750 m²

therefore,

• Area of triangular field would be 33750 m² .