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?

Question

10113 views around the world

You can reuse this answer
Creative Commons License

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