A rectangular field is of dimension 20m x 15m. Two paths run parallel to the sides of the rectangle through the centre of the field. The width of the longer path is 2 m and that of the shorter path is 1m. Find (i) the area of the paths (ii) the area of the remaining portion of the field (iii) the cost of the constructing the roads at the rate of Rs.10 per sq.m.
Answers
Answer:
210 is the answer of this
The area of the paths is 53 m² .
The area of the remaining portion of the field is 247 m².
The cost of constructing the roads at the rate of 10 per sq.m is Rs. 530.
Step-by-step explanation:
Dimensions of rectangular field is 20 m x 15 m
The width of the longer path is 2 m and that of the shorter path is 1 m
Step 1:
The area of the rectangle ABCD = length * breadth = 20 * 15 = 300 m²
Area of the shorter path IJKL = 15 * 1 = 15 m²
Area of the longer path EFGH = 20 * 2 = 40 m²
and,
Area of the middle common path MNOP = 2 * 1 = 2 m²
∴ Area of the paths is given by,
= [Area of the shorter path IJKL] + [Area of the londer path EFGH] - [Area of the middle common path MNOP]
= 15 + 40 - 2
= 53 m²
Step 2:
∴ Area of the remaining portion is given by,
= [The area of the rectangle ABCD] - [Area of the paths]
= 300 - 53
= 247 m²
Step 3:
The rate of constructing the roads is given as Rs. 10 per sq. meter
∴ The total cost of constructing the roads is given by,
= 53 m² * Rs. 10
= Rs. 530
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