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CBSE Class 6 Mathematics Question 13 of 26

Playing with Constructions — Question 13

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13
Question
Give the lengths of the sides of a rectangle that cannot be divided into: (Page 201) (i) Two identical squares (ii) Three identical squares.
Answer

(i) Let the smaller side of a rectangle be x cm. If the larger side of the rectangle is 2x cm (x cm + x cm), then this rectangle can be divided into two identical squares of side x cm. (Fig. 1)
Let us consider a rectangle of sides 4 cm and 6 cm. Here, 6 is not equal to 8 (4 + 4), so, it cannot be divided into two identical squares as shown in Fig. 2
(ii) Let the smaller side of a rectangle be x cm. If the larger side of the rectangle is 3x cm (x cm + x cm + x cm), then this rectangle can be divided into three identical squares of side x cm. (Fig. 3)
Let us consider a rectangle of sides 3 cm and 8 cm. Here, 8 is not equal to 9 (3 + 3 + 3), so, it cannot be divided into three identical squares as shown in Fig. 4.
8.4 An Exploration in Rectangles Construct (Page No. 201 – 203)