Question

Matthew has 170 tiles he can use for this project. Identify the largest patio design that he can make. Show or explain your reasoning.

Answer 1

Answer:

Design 12

Step-by-step explanation:

See attached for missing part of the question

As we see each design comprises of:

• Entrance and exit- each one tile
• Design 1 has 1 row and 3 columns,
• Design 2 has 2 rows and 4 columns,
• Design 3 has 3 rows and 5 columns.

So design x has x rows and (x+2) columns.

We can put it as equation to get 170 tiles:

• x(x+2) + 2 = 170
• x² + 2x - 168 = 0

Solving the quadratic equation we get:

• x = 12

So design 12 has 12 rows, 14 columns, 1 entrance and 1 exit tiles.

• 12*14 + 2 = 170