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Question
A rectangular field is of dimension 20 m × 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 (i) the area of the paths (ii) the area of the remaining portion of the field (iii) the cost of constructing the roads at the rate of ₹ 10 per sq.m
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Solution
Length of the rectangular field L = 20 m
Breadth B = 15 m
Area = L × B
= 20 × 15 m2
Area of outer rectangle = 300 m2 
Area of inner small rectangle = `19/2 xx 13/2` = 61.75 cm2
(i) Area of the path = Area of the outer rectangle – Area of 4 inner small rectangles
= 300 – 4(61.75)
= 300 – 247
= 53 m2
Area of the paths = 53 m2
(ii) Area of the remaining portion of the field
= Area of the outer rectangle – Area of the paths
= 300 – 53 m2
= 247 m2
Area of the remaining portion = 247 m2
(iii) Cost of constructing 1 m2 road = ₹ 10
∴ Cost of constructing 53 m2 road = ₹ 10 × 53 = ₹ 530
∴ Cost of constructing road = ₹ 530
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