Mathematics
A triangular park ABC has sides 120 m, 80 m and 50 m (as shown in the adjoining figure). A gardner Dhania has to put a fence 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 ₹ 20 per metre leaving a space 3 m wide for a gate on one side.
![A triangular park ABC has sides 120 m, 80 m and 50 m (as shown in the adjoining figure). A gardner Dhania has to put a fence 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 ₹ 20 per metre leaving a space 3 m wide for a gate on one side. Mensuration, ML Aggarwal Understanding Mathematics Solutions ICSE Class 9.](https://cdn1.knowledgeboat.com/img/mla9/q19-c16-ex-16-1-mensuration-ml-aggarwal-solutions-icse-class-9-1200x525.png)
Mensuration
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Answer
It is given that,
ABC is a triangular park with sides 120 m, 80 m and 50 m.
Here, the perimeter of △ABC = 120 + 80 + 50 = 250 m
Portion at which a gate is built = 3m
Remaining perimeter = 250 – 3 = 247 m.
So, the length of the fence around it = 247 m.
Rate of fencing = ₹20 per metre
Total cost of fencing = 20 × 247 = ₹4940.
We know that,
Semi perimeter (s) = = 125 cm.
Area of triangle =
Substituting values we get,
Hence, area needed for plantation = m2 and cost of fencing = ₹4940.
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