If the tiny square has $3cm$ side, what would be the total area of the big rectangle?

Question

If the tiny square has $3cm$ side, what would be the total area of the big rectangle?

Answer 1

Googleing "rectangle of squares", I've found the solution. You can just start calling some side $x$ and writing out everything you know, using pretty much only that the four sides of a square have equal length. You get:

I found it here: http://www.pleacher.com/mp/probweek/p2016/a0316a.html You can find $x$ by equating the top and the bottom of the rectangle. You'll get: $65 \times 47 = 3055$.

Answer 2

Choose a square (near the $3$) and call it $x$ keep doing linear algebra until you get an equation that $x$ satisfies.

Answer 3

The solution appears at the top of the Mathworld page Perfect Rectangle, which in turn has a link to a database of solutions. The area is $3055$.

In the database it's found under Simple Perfect Squared Rectangles, where it's one of just six rectangles that can be formed using exactly $10$ squares of distinct sizes.