Question

a triangular park has sides 60 m , 100 m and 140 m . a gardener has to put fence all around it and also plant grass inside. how much area does he needed to plant ? Find the cost of fencing it with barbed wire at the rate of rs. 10 per meter leaving a space of 1 m for gate on one side​

Answer 1

Given :

• Sides of a Triangular Park are 60 m , 100 m , 140 m.

To Find :

• Cost of fencing it with wire at the rate of Rs. 10 after leaving a space of 1 m for gate.

Solution :

• a = 60m.
• b = 100m.
• c = 140m.

$\longmapsto\tt{s=\dfrac{a+b+c}{2}}$

$\longmapsto\tt{s=\dfrac{60+100+140}{2}}$

$\longmapsto\tt{s=\cancel\dfrac{300}{2}}$

$\longmapsto\tt\bf{s=150\:m}$

Now ,

$\longmapsto\tt{Area=\sqrt{s(s-a)(s-b)(s-c)}}$

$\longmapsto\tt{\sqrt{150(150-60)(150-100)(150-140)}}$

$\longmapsto\tt{\sqrt{150(90)(50)(10)}}$

$\longmapsto\tt{\sqrt{5\times{3}\times{5}\times{2}\times{3}\times{3}\times{5}\times{2}\times{5}\times{5}\times{2}\times{5}\times{2}}}$

$\longmapsto\tt{5\times{3}\times{2}\times{5}\times{5}\times{2}\sqrt{3}}$

$\longmapsto\tt\bf{1500\sqrt{3}\:{m}^{2}}$

Now ,

$\longmapsto\tt{Total\:Area\:of\:Park=300-1}$

$\longmapsto\tt\bf{299\:m}$

Cost of Fencing it at Rs. 10 :

$\longmapsto\tt{299\times{10}}$

$\longmapsto\tt\bf{Rs.2990}$

So , The Cost of Fencing Park is Rs. 2990..