A series of squares follows a "stair-step" pattern as shown. The smallest square is 1 unit on a side. The side of each larger square is twice as long as the side of the previous square. How many squares must be arranged this way if the total area of these squares is 1,365 square units?
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Answer:
6 cm
Step-by-step explanation:
Let x = side of smaller square
Let 2x = side of larger square
Therefore, we can create an equation (x)² + (2x)² = 45
Solving for x:
(x)² + (2x)² = 45
x² + 4x² = 45
5x² = 45
x² = 9
x = 3
Side Length of Larger Square = 2x = 2(3) = 6 cm
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