Two triangular plots are similar in shape, their corresponding sides being in the ratio 3 : 5. The smaller plot has an area of 63 square metres. What is the area of the larger plot, in square metres?

For similar figures the areas are in the ratio of the SQUARES of corresponding sides, so the larger area = $63\times (5/3{)}^2=63\times 25/9=175$ sq m. The trap $105=63\times 5/3$ scales the area by the linear ratio, which is the single commonest error here; $315=63\times 5$ multiplies by the larger term alone; $525=63\times 25/3$ squares the 5 but forgets to square the 3.