Question

A triangular park has side 120m ,80m, 50m 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 rate of rs.20 per meter leaving a space of 3m wide for a gate on 1 side

Answer 1

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Answer 2

Answer:

Area to be planted $A=1452.3 m^2$

Cost of the fencing = Rs.4940

Step-by-step explanation:

Given : A triangular park has side 120m ,80m, 50m.

Barbed wire at rate of Rs.20 per meter.

To find : The area of park he need to plant and the cost of fencing leaving a space of 3m wide for a gate on 1 side.

Solution : First we the area by Heron's formula,

$A=\sqrt{s(s-a)(s-b)(s-c)}$

Where s is $s=\frac{a+b+c}{2}$

a= 120m, b=80m, c=50m

Substitute the value,

$s=\frac{a+b+c}{2}$

$s=\frac{120+80+50}{2}$

$s=\frac{250}{2}$

$s=125m$

Now, The area to be planted is

$A=\sqrt{s(s-a)(s-b)(s-c)}$

$A=\sqrt{125(125-120)(125-80)(125-50)}$

$A=\sqrt{125(5)(45)(75)}$

$A=\sqrt{2109375}$

$A=1452.3 m^2$

Length of the fenced = Perimeter- space for the gate

Perimeter= a+b+c= 120+80+50=250

Space for the gate is = 3m

Length of the fenced = 250-3 = 247 m

Cost of the fencing = Length of the fence × Wire rate

Cost of the fencing = 247 × 20 = Rs.4940