# The combined area of two squares is 20 square centimeters. Each side of one square is twice as long as a side of the other square. How do you find the lengths of the sides of each square?

The squares have sides of 2 cm and 4 cm.

To represent the squares' sides, define variables.

The areas add up to 20 cm^2.

The larger square has four centimeter sides, while the smaller square has two.

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Let's denote the length of the side of the smaller square as ( x ) cm. Since the length of a side of the larger square is twice as long, its side length would be ( 2x ) cm.

The area of a square is given by the formula: ( \text{Area} = (\text{Side length})^2 ).

Given that the combined area of the two squares is 20 square centimeters, we can write the equation:

[ x^2 + (2x)^2 = 20 ]

Simplify and solve for ( x ):

[ x^2 + 4x^2 = 20 ]

[ 5x^2 = 20 ]

[ x^2 = 4 ]

[ x = 2 ]

So, the side length of the smaller square is 2 cm, and the side length of the larger square is ( 2 \times 2 = 4 ) cm.

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