MathematicsA rectangular field is 50 m by 40 m. It has two roads through its center, running parallel to its sides. The width of the longer and the shorter roads are 2 m and 2.5-m-respectively. What is the area of the roads and the area of the remaining portion of the field?

A rectangular field is 50 m by 40 m. It has two roads through its center, running parallel to its sides. The width of the longer and the shorter roads are 2 m and 2.5-m-respectively. What is the area of the roads and the area of the remaining portion of the field?


  1. A
    195 and 1805 m2
  2. B
    1805 and 195 m2
  3. C
    1200 and 200 m2
  4. D
    200 and 1200 m2 

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    Solution:

    Given that, the dimension of the rectangle is 50m by 40m. The width of the longer and the shorter roads are 2 m and 2.5-m-respectively.
    The area of the roads = (Length × Width of longer road) + (Breadth × Width of shorter road) − (Total area of rectangular field).
    ⇒(50×2)+(40×2.5)-(2×2.5)
    ⇒100+100-5
    ⇒195m2
    Calculating the remaining portion of the field = Total area of rectangle − the area of the roads.
    ⇒(50×40)-195
    ⇒2000-195
    ⇒1805m2
    The area of the remaining portion of the field is 1805 m2 and the area of the roads is 195 m2.
    Therefore, the correct answer is option 1.
     

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