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?

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Answer 1 · 2016-11-14T07:05:24

The squares have sides of 2 cm and 4 cm.

Define variables to represent the sides of the squares.

Let the side of the smaller square be #x# cm
The side of the bigger square is #2x# cm

Find their areas in terms of #x#

Smaller square: Area = #x xx x = x^2#
Bigger square: Area = #2x xx 2x = 4x^2#

The sum of the areas is #20 cm^2#

#x^2 +4x^2 = 20#

#5x^2 = 20#

#x^2 = 4#

#x = sqrt4#

#x = 2#

The smaller square has sides of 2 cm
The bigger square has sides of 4cm

Areas are: #4cm^2+16cm^2 = 20cm^2#