A child is given two large squares, ten small squares, and nine rectangle whose length and width are those of the squares. Show with an illustration how the child can make one complete rectangle using all 21 pieces. (Hint: Let x=side of large square, y=side of small square)
I worked this out algebraically
Let the little squares be x*x and the big ones are y*y so the long ones are x*y
Ths sum of the areas is
I want two numbers that multiply to 10*2=20 and add to 9 Those numbers are 4 and 5
\(10x^2+9xy+2y^2\\ =10x^2+5xy+4xy+2y^2\\ =5x(2x+y)+2y(2x+y)\\ =(5x+2y)(2x+y)\\\)
So one side is 5x+2y long and the other is 2x+y long
Now it is quite easy. If you have problems then assign a number to x and to y.
I chose 1 and 7 but any numbers that have only 1 as a factor will do.
People ususally find it easier to deal with real numbers instead of with pronumerals