Black and white squares are used to form figures that follow a pattern.
The first three figures are shown below.
What is the ratio of black squares to white squares used to form Figure 12?
Ans: ______________ [2]
Fig 1:
| Number of black squares | = $5$ |
| Number of white squares | = $4$ |
Fig 2:
| Number of black squares | = $5 + 4 × 1$ |
| Number of white squares | = $4 × 2$ |
Fig 3:
| Number of black squares | = $5 + 4 × 2$ |
| Number of white squares | = $4 × 3$ |
Hence,
Fig 12:
| Number of black squares | = $5 + 4 × 11 = 49$ |
| Number of white squares | = $4 × 12 = 48$ |
| Ratio of black squares to white squares | = $\boxed{49:48}$ |
Fig 1:
| Number of black squares | = $1 + 4$ |
| Number of white squares | = $4$ |
Fig 2:
| Number of black squares | = $1 + 4 × 2$ |
| Number of white squares | = $4 × 2$ |
Fig 3:
| Number of black squares | = $1 + 4 × 3$ |
| Number of white squares | = $4 × 3$ |
Hence,
Fig 12:
| Ratio of black squares to white squares | = $(1 + 4 × 12) : (4 × 12)$ |
| = $\boxed{49:48}$ |
