# 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?

Nov 14, 2016

The squares have sides of 2 cm and 4 cm.

#### Explanation:

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 $2 x$ cm

Find their areas in terms of $x$

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

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

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

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

${x}^{2} = 4$

$x = \sqrt{4}$

$x = 2$

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

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