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An artist is using tiles and boards for a project. A tile has length one-fourth

ft and width one-fourth

ft. A board has length one-sixth yd

and width one-sixth yd

. What is the ratio of the length of the tile to the length of the​ board? What is the ratio of the area of the tile to the area of the​ board?

Respuesta :

bhuvna789456

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

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