Question

Hari Prasad’s triangular field has sides of 90m, 80m and 70m. How much barbed wire will he need for fencing the field if he uses 6 lengths of wire along each side? How much will he have to pay for the wire if it costs Rs.50 per metre?

Answer 1

Hint: We can add the given sides to get the perimeter of the triangle. Then to find the total length of the wire, we must take six times the perimeter. Then we can find the cost of fencing by multiplying the cost of the wire per metre with the total length of wire.

Complete step-by-step answer:
We are given that the 3 sides of a triangular field are of 90m, 80m and 70m. The perimeter of a triangle is given by the sum of all the three sides.

$\Rightarrow Perimeter=a+b+c$
On substituting the given value, we get
$\Rightarrow Perimeter=90+80+70$
On doing the additions, we get
$\Rightarrow Perimeter=240m$
According to the question, 6 lengths of wire is used for fencing each side. So the length of the total wire required is 6 times the perimeter.
$\Rightarrow l=6\times perimeter$
On substituting the value of perimeter, we get
$\Rightarrow l=6\times 240m$
On multiplication we get,
$\Rightarrow l=1440m$
So, the length of the wire required for fencing the field is$1440m$.
We are given that 1 metre of the wire cost Rs.50. So we get the total cost by multiplying the length of the wire with the cost of one metre of wire.
$\Rightarrow \text{Cost}=50\times l$
On substituting the length of the wire, we get
$\Rightarrow \text{Cost}=50\times 1440$
After multiplication, we get
$\Rightarrow \text{Cost}=72000$
Therefore, the cost of fencing the field is Rs.72000.

Note: We must understand that the fencing is done along the boundary and the length of the boundary is given by the perimeter. The perimeter of a body is the sum of the length of all the sides of the body. We use the concept of perimeter while reforming a wire to form different shapes, fencing or walking or running around something etc. We must take care that the six length of the wire is used for fencing one side. As all the lengths are in metres and the cost is also given per metre we need not to convert any units. Otherwise, in this kind of problem we must take care of the units and necessary conversions must be done.