Question

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

Answer 1

Given:

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

To Find:

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

Solution:

Let the sides of triangular park be

• Side a = 120m
• Side b = 80m
• Side c = 50m

Area of Traingle = √s (s -a) (s - b) (s - c)

➠ Side = a + b + c/2

➠ Side = 120 + 80 + 50/2

➠ Side = 250/2

➠ Side = 125 m

Now, Area of triangular park

➠ Area = √s (s -a) (s - b) (s - c)

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

➠ Area = 315 √15m²

• Area needed to plant = 315 √15m²

Now, Finding cost of fencing

➠ Number of metres = 250 - 3

➠ Number of metres = 247 m

Cost of fencing = Rs.2 per metre

Cost of fencing park = Rs. 20 × 247

• Cost of fencing park = Rs. 4940

Answer 2

Answer:

HOPE IT IS HELPFUL

Step-by-step explanation:

The sides of the triangular park are 120 m, 80 m and 50 m.



Perimeter of the triangular park = 120m + 80 m + 50 m= 250 m

Therefore, it's semi-perimeter (s) = 250/2 = 125 m

Now, we will use Heron’s formula to find the area of a triangle;

Area of a triangle = s(s−a)(s−b)(s−c)−−−−−−−−−−−−−−−−−√s(s−a)(s−b)(s−c)

Here, a = 120 m, b = 80 m, c = 50 m, and s = 125 m

Now, putting these values in the above formula:

= 125(125−120)(125−80)(125−50)−−−−−−−−−−−−−−−−−−−−−−−−−−−−√125(125−120)(125−80)(125−50)

=125×5×45×75−−−−−−−−−−−−−−√=125×5×45×75

=2109375−−−−−−−√=2109375

= 1452.36 sq. m

Hence, the gardener has to plant grass in 1452.36m²

Now we have to find the cost of fencing the field with a barbed wire at the rate of Rs. 20 per m leaving a space of 3m wide for a gate.

Therefore, the gardener has to fence = 250 – 3= 247m

So, total cost of fencing at the rate of Rs. 20 per meter = 247 × 20= Rs. 4940