A square field is of side 50 m. It has two roads through its centre, running parallel to its sides and at right angles to each other. The width of the two roads are 3 m and 3.75 m respectively. Find the area of the roads and the area of the remaining portion of the field.
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Step-by-step explanation:
Let ABCD be the rectangular field and KLMN and PQRS the two rectangular roads with width 1.8 m and 2.5 m, respectively.
Given that length of rectangular field = 50 m
Breadth of rectangular field = 40m
Area of rectangular field ABCD = 50 m x 40 m
= 2000 m^2
Area of the road KLMN = 40 m x 2.5 m
= 100 m^2
Area of the road PQRS = 50 m x 1.8 m
= 90 m^2
Clearly area of EFGH is common to the two roads.
Thus, Area of EFGH = 2.5 m x 1.8 m = 4.5 m^2
Hence, Area of the roads = Area of KLMN + Area of PQRS – Area of EFGH
= (100 m^2 + 90 m^2) – 4.5 m^2
= 185.5 m^2
Area of the remaining portion of the field = Area of the rectangular field ABCD – Area of the roads
= (2000 – 185.5) m^2
= 1814.5 m^2