Question

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

Answer 1

$\large{\underline{\underline{\bold{\red{\sf{Question}}}}}}$

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

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$\large{\underline{\underline{\bold{\blue{\sf{Solution:.}}}}}}$

For finding area we have ,

Sides of Triangle

a →120m , b → 80m , c → 50m

Semi→

$\dfrac{50m+80m+120m}{2}⇒\cancel\dfrac{250}{2}⇒125m$

$Area⇒\sqrt{s (s-a) (s-b) (s-c)}$

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

$\sqrt{125 × 5 × 45 × 75}$

→${\boxed{\bf\red{375\sqrt{15m}^{2}}}}$

Perimeter of the park = 250m

Length of the wire needed for fencing⇒$250-3$

→$247m$

Cost of fencing 247m area at ₹20

$Rs.20 × 247$

→$\large{\underline{\underline{\bold{\green{\sf{Rs.4940}}}}}}$

Answer 2

$\large{\frak{\purple{Solution}}}$

Using the Heron's formula for finding the area of triangular park.

sides of triangle are:

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

semi perimeter , s = (a+b+c)/2

s = (120+80+50)/2 = 125 m

$\bf Heron's\: formula = \sqrt{s(s-a)(s-b)(s-c)} \\\\\bf putting\:values\\\\\bf ar(\triangle park) = \sqrt{125(125-120)(125-80)(125-50)} \\\\\bf ar(\triangle park) = \sqrt{125\times5\times45\times75}\\\\\bf ar(\triangle park) = 375 \sqrt{15}\:m^2$

so, Dhania need to plant 375√15 m² of area.

_____________________________________________

Now, finding the perimeter of park

perimeter of park = 120 + 80 + 50

perimeter of park = 250 m

it is given that a space 3 m wide is not fenced

hence,

perimeter to be fenced = 250 - 3 = 247 m

rate of fencing = Rs 20 / m

so,

cost of fencing 247 m = 247 * 20 Rs

cost of fencing 247 m  =4940 Rs.