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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)

 Jan 23, 2022
 #1
avatar+117100 
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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 

 \(10x^2+9xy+2y^2\\ \)

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

 Jan 28, 2022
 #2
avatar+117100 
+1

I have just looked at you post record.

It seems that so far you have never responded to an answer.

Perhaps this is why it took you five days to get an answer here.

 

You are expected to respond to your answerers.

 Jan 28, 2022

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