Question

a triangular park ABC has side 120m, 80m, and 50m (see Fig.12.7). 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 Rs20 per metre living space 3m wide for a gate on one side.​

Answer 1

Step-by-step explanation:

here, a=120m,

b=80m,

c=50m

and, s= (a+b+c)/2 = 250/2 = 125

Area she need to plant grass =

√s(s−a)(s−b)(s−c)

= √125(125−120)(125−80)(125−50)

=375 √15 m²

cost of fencing =[(a+b+c)−3]*20

=[250−3]*20

=Rs4940

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Answer 2

★ Solution :-

◆ We know that,

↦ Semi - perimeter of triangle = a + b + c / 2

Now, substitute the values :-

↦ 50 + 80 + 120 / 2

↦ 250 / 2

↦125 m

◆ We also know that,

↦ Area of a triangle = √s(s-a)(s-b)(s-c)

Now, substitute the values :-

↦ √125(125 - 50) (125 - 80) (125 - 120)

↦ √125 × 75 × 45 × 5 m²

↦ 375√15 m²

↦ Also, Perimeter of the park = AB + BC + CA = 250 m

↦ Therefore, length of the wire needed for fencing = 250 m - 3 m ( to be left for gate )

↦ 247 m

↦ And, So the cost of fencing = ₹ 20 × 247 = ₹4940

■ Hence, the cost of fencing is ₹4940.