Q1.
Which of these rectangles requires more rangoli powder to be coloured, if the colouring is done evenly?
Answer
The 7 cm × 4 cm rectangle.
7 cm × 4 cm rectangle: 7 × 4 = 28 unit squares
8 cm × 3 cm rectangle: 8 × 3 = 24 unit squares
28 > 24, so the first rectangle needs more powder.
8 cm × 3 cm rectangle: 8 × 3 = 24 unit squares
28 > 24, so the first rectangle needs more powder.
Why it happens: if the colouring is even, the powder used is proportional to the region's area, not to how long or how wide it looks. Counting the non-overlapping 1 cm squares that pack into each rectangle is exactly what measuring area means — and 4 rows of 7 squares is 28 squares, while 3 rows of 8 squares is only 24.
Notice: both rectangles have almost the same perimeter (22 cm and 22 cm). Equal perimeters, unequal areas — the very point made on the next page.