NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 6: Mensuration - Multiple Choice Questions
Question 2

Question.  2

A square shaped park ABCD of side 100 m has two equal rectangular flower beds each of size 10 m × 5 m (Fig. 6.5). Length of the boundary of the remaining park is

(A)

360 m

(B)

400 m

(C)

340 m

(D)

460 m

Detailed Answer with Explanation:

  1. The park is a square with side (100, ext{m}).
    Perimeter of a square: (4 imes ext{side}).
    So, outer boundary (= 4 imes 100 = 400, ext{m}).
  2. There are two rectangular flower beds inside the park (they do not touch the outer edge).
    When a bed is inside, its edges also become part of the boundary of the remaining park (like the edge of a hole).
  3. Size of each bed: (10, ext{m} imes 5, ext{m}).
    Perimeter of a rectangle: (2 imes ( ext{length} + ext{width})).
    For one bed: (2 imes (10 + 5) = 2 imes 15 = 30, ext{m}).
  4. There are two such beds, so added inner boundary (= 2 imes 30 = 60, ext{m}).
  5. Total boundary of the remaining park (=) outer boundary (+) inner boundaries.
    (400 + 60 = 460, ext{m}).

Answer: (460, ext{m}) — Option D.

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NCERT Exemplar Solutions Class 6 – Mathematics – Unit 6: Mensuration – Multiple Choice Questions | Detailed Answers