Ratio of the length of the tile to the length of the board is 1:2
Ratio of the area of the tile to the area of the board is 1:4
Step-by-step explanation:
- Step 1: Find ratio of length of the tile to the length of the board
Length of the tile = 1/4 ft
Length of the board = 1/6 yd = 1/6 × 3 = 1/2 ft (∵ 1 yd = 3ft)
∴ Ratio of length of the tile to length of the board = 1/4 : 1/2 = 1/4 × 2/1 = 1:2
- Step 2: Find the ratio of area of the tile to area of the board
Area of the tile = Length × Width = 1/4 ft × 1/4 ft = 1/16 ft²
Area of the board = Length × Width = 1/6 yd × 1/6 yd
= 1/2 ft × 1/2 ft (∵ 1 yd = 3 ft)
= 1/4 ft²
⇒ Ratio of the area of the tile to the area of the board = 1/16 : 1/4
= 1/16 × 4/1 = 1:4
