Question

A triangle park ABC has sides 120m, 80m and 50m.A gardeneer dhania has to put a fence all around it and also plant grass inside. How much area does she need to plant? Find the cost of fencing it with barbed wire at the rate of Rs 20 per metre leaving space 3m wide for a gate on one side. ​

Answer 1

Given that:

• A triangular park ABC has sides 120 m, 80 m and 50 m.
• A gardener Dhania has to put a fence all around it and also plant grass inside.

To Find:

• How much area does she need to plant?
• Find the cost of fencing it with barbed wire at the rate of Rs 20 per metre leaving space 3 m wide for a gate on one side.

We know that:

Heron's Formula to find area of a triangle,

• A = √[s(s - a)(s - b)(s - c)]

Formula for perimeter of a triangle,

• P = a + b + c

Where,

• a, b, and c are three sides of the triangle.
• A = Area
• P = Perimeter
• s = Semi perimeter

We have:

• a = 120 m
• b = 80 m
• c = 50 m

Finding the perimeter of the triangular park:

↣ P = 120 + 80 + 50

↣ P = 250

∴ Perimeter = 250 m

Finding the semi perimeter:

↣ s = P/2

↣ s = 250/2

↣ s = 125

∴ Semi perimeter = 125 m

Finding the area of the triangular park:

↣ A = √[125(125 - 120)(125 - 80)(125 - 50)]

↣ A = √[125 (5) (45) (75)]

↣ A = √[5 × 5 × 5 × 5 × 3 × 3 × 5 × 3 × 5 × 5]

↣ A = 5 × 5 × 3 × 5 × √(5 × 3)

↣ A = 375√15

∴ Area = 375√15 m²

Hence,

• She needs to plant 375√15 m² of area.

Finding the length of wire to fence the park:

Length = Perimeter - leaving space

↣ Length = 250 - 3

↣ Length = 247

∴ Length of wire = 247 m

Finding the cost of fencing the park:

• Cost of 1 m of wire = Rs 20
• Cost of 247 m of wire = Rs (20 × 247)
• Cost of 247 m of wire = Rs 4940

Hence,

• The total cost of fencing the triangular park with barbed wire is Rs 4940.

Answer 2

Given :-

A triangle park ABC has sides 120m, 80m and 50m.A gardeneer dhania has to put a fence all around it and also plant grass inside.

To Find :-

Cost of fencing it with barbed wire at the rate of Rs 20 per metre leaving space 3m wide for a gate on one side.

Solution :-

We know that

S = a + b + c/2

S = 120 + 80 + 50/2

S = 250/2

S = 125 m

Area = √s(s - a)(s - b)(s - c)

Area = √125(125 - 120)(125 - 80)(125 - 50)

Area = √125(5)(45)(75)

Area = √21,09,375

Area = 1452.3 m²

Perimeter = a + b + c

Perimeter = 120 + 80 + 50

Perimeter = 250 m

Space left = 3 m

Remaining space = 250 - 3 = 247 m

Cost of fencing = Rate × Perimeter

Cost of fencing = 20 × 247

Cost of fencing = Rs. 4940