A square tile is 10 cm on each side. Ravi says if you double the side to 20 cm, the area doubles too

Why

Ravi is matching the change in the area to the change in the side — double one, double the other — which is how many everyday quantities behave, but not area. Area is side MULTIPLIED by side, so when the side doubles, both of the things being multiplied double, and 2 times 2 is 4. The 10 cm tile has an area of 10 times 10, which is 100 square cm; the 20 cm tile has 20 times 20, which is 400 square cm — four times 100, not two times. Picture the big tile: exactly four of the small tiles fit inside it, two across and two down. Test: triple the side instead, to 30 cm, and the area goes to 30 times 30, which is 900 — nine times the original, the multiplier squared again. Sara is right, the area becomes four times as big: when a shape is scaled up, its area grows by the scale factor multiplied by itself.