Question

Suppose a triangular park in your local has sides 120m, 80m, and 50m. You want to put a fence all around it and also plant grass inside. How much area do you need to plant? Also find the cost of fencing it with wire at the rate of Rs. 20 per meter leaving 3m wide space for a gate.​

Answer 1

Answer:

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)−−−−−−−−−−−−−−−−−√

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)−−−−−−−−−−−−−−−−−−−−−−−−−−−−√

=125×5×45×75−−−−−−−−−−−−−−√

=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

Note:Heron’s formula is used when the length of all the sides of a triangle is given. Heron’s formula is equal to s(s−a)(s−b)(s−c)−−−−−−−−−−−−−−−−−√ where s is the half of a perimeter of a triangle, and a, b, and c is the sides of a triangle.