Question 5 of 12intermediate💡 UnderstandShort Answer2 marks

Give the lengths of the sides of a rectangle that cannot be divided into— two identical squares; three identical squares.

Correct Answer

Rule for Two Identical Squares: A rectangle can be divided into two identical squares only if its length is twice its width (2:1 ratio).

Rule for Three Identical Squares: A rectangle can be divided into three identical squares only if its length is three times its width (3:1 ratio).

Examples that CANNOT be divided into two identical squares:

  • 5 cm × 3 cm
  • 7 cm × 4 cm
  • 10 cm × 6 cm (Any rectangle where length ≠\neq 2 × width)

Examples that CANNOT be divided into three identical squares:

  • 5 cm × 2 cm
  • 8 cm × 3 cm
  • 10 cm × 4 cm (Any rectangle where length ≠\neq 3 × width)
Exercise: Construct (Breaking Rectangles) | Q: 1 | (Page Page 15)
For More Understanding

Explanation

The chapter establishes that for a rectangle to be divided into n identical squares, the ratio of length to width must be n:1. Any rectangle not satisfying this condition cannot be divided into n identical squares.

Solution Steps

  1. For two identical squares: length must equal 2 × width (2:1 ratio)

  2. For three identical squares: length must equal 3 × width (3:1 ratio)

  3. Any rectangle where length ≠\neq 2 × width cannot be divided into two identical squares

  4. Any rectangle where length ≠\neq 3 × width cannot be divided into three identical squares

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