Give the lengths of the sides of a rectangle that cannot be divided into — Class 6
Give the lengths of the sides of a rectangle that cannot be divided into — Class 6
Question 1.
Give the lengths of the sides of a rectangle that cannot be divided into — Class 6
- two identical squares;
- three identical squares.
Solution:
For two identical squares, lengths of the sides of the rectangle can be say 2.5 cm, 3.7 cm, 5.9 cm, etc. because using a ruler, it will not be possible to measure the lengths
[latex]\frac{2.5}{2}[/latex] = 1.25 cm,[latex]\frac{3.7}{2}[/latex] = 1.85 cm, [latex]\frac{5.9}{2}[/latex] = 2.95 cm, etc.
For three identical squares, lengths of the sides of the rectangle can not be say 10 cm, 16 cm, 20 cm, 2.8 cm, 3.5 cm etc. (Reason same as with case of two squares.)
Question 2.
A Square within a Rectangle Class 6
Construct a rectangle of sides 8 cm and 4 cm. How will you construct a square inside, as shown in the fiure, such that the centre of the square is the same as the centre of the rectangle?
Hint : Draw a rough figure. What will be the sidelength of the square? What will be the distance between the corners of the square and the outer rectangle?
Solution:
Side length of the square will be 4 cm each. Distance between the corners of the square and the outer rectangle will be [latex]\frac{8-4}{2}[/latex] = 2 cm each.