Four Squares

A rectangle with side lengths a and 20 is divided into 4 squares as shown. What is the value of a?
image
Source: NCTM Mathematics Teacher, December 2005

SOLUTION
image
Sum of the areas of the 4 squares equals the area of the rectangle
a^2+(2x)^2+x^2+x^2=20a
a^2+6x^2=20a
(3x)^2+6x^2=20(3x)
9x^2+6x^2=60x
15x^2-60x=0
15x(x-4)=0
x=0 (extraneous solution) or x=4
a=3x=3(4)=12

Answer: 12 units

Alternative solution
Sum of a side length of the large square and a side length of the medium square equals the length of the rectangle
3x+2x=20
5x=20
x=4

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About mvtrinh

Retired high school math teacher.
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