U CIUI
3. A rectangular field is of dimension 20 m x 15 m. 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 1 m.
Find the:
a. area of the paths.
b. area of the remaining portion of the field.
C. cost of constructing the roads at the rate of 10 per m².
Answers
Answer:
Step-by-step explanation:
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 londer path EFGH = 20 * 2 = 40 m^2
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 protion 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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