Residence Association is planning to develop a park in the colony. The rectangular park of dimensions 75m × 25m consists a path of uniform width along its boundary in the out side to develop walking habit among the residents of the colony. To beautify the park, 5 square flower beds are made in the park by spending 10% of the total cost of 5 lakh rupees for Rs.2500 per sq m.
1. The expression for finding the area of the path
x²+100x+1875
4x²+200x+1875
x²+100x
4x²+200x
2. The cost of constructing a 1m wide path at Rs. 1250 per sq m
Rs. 25500
Rs. 255000
Rs. 55000
Rs. 25000
3. The distance travelled by a person if he completes 10 rounds along the inner boundary of the path
2km
20km
200km
2000km
4. The side of each square flower bed
4m
2m
20m
40m
Answers
Answer:
a: 4x²+200x
b: 25000
c: 2km
d: 2m
Given : The rectangular park of dimensions 75m × 25m consists a path of uniform width along its boundary in the out side to develop walking habit among the residents of the colony.
To find : 1. The expression for finding the area of the path
The cost of constructing a 1m wide path at Rs. 1250 per sq m
Solution:
park of dimensions 75m × 25m
path out side of width x m , all side
Hence outer boundaries 75 + 2x , 25 + 2x
Area of path = ( 75 + 2x) (25 + 2x) - 75 * 25
= 150x + 50x + 4x ² + 75 * 25 - 75 * 25
= 4x² + 200x
The expression for finding the area of the path = 4x² + 200x
1m wide path Hence area of path = 4(1)² + 200(1)
= 204 m²
Rate = 1250 per sq m
Hence cost = 204 * 1250 = 2,55,000
distance travelled by a person if he completes 10 rounds along the inner boundary of the path = 10 * 2 ( 75 + 25) = 2000 m = 2 km
5 square flower beds are made in the park by spending 10% of the total cost of 5 lakh rupees for Rs.2500 per sq m.
Spend = (10/100) 500000 = 50000
5 square flower beds
=> cost on one flower bed =50000/5 = 10000
Rs.2500 per sq m.
Hence area of one flower bed = 10000/2500 = 4 m²
The side of each square flower bed = √4 = 2 m
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