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 $x$ $x$ cm
The side of the bigger square is $2 x$ $2x$ cm

Find their areas in terms of $x$ $x$

Smaller square: Area = $x \times x = x^{2}$ $x xx x = x^2$
Bigger square: Area = $2 x \times 2 x = 4 x^{2}$ $2x xx 2x = 4x^2$

The sum of the areas is $20 c m^{2}$ $20 cm^2$

$x^{2} + 4 x^{2} = 20$ $x^2 +4x^2 = 20$

$5 x^{2} = 20$ $5x^2 = 20$

$x^{2} = 4$ $x^2 = 4$

$x = \sqrt{4}$ $x = sqrt4$

$x = 2$ $x = 2$

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

Areas are: $4 c m^{2} + 16 c m^{2} = 20 c m^{2}$ $4cm^2+16cm^2 = 20cm^2$