Purpose of The Question
The following question is most appropriate for students within a high school Geometry course, as this particular question calls for the application of geometric concepts along with algebra. The connection between these two applications can often be a hard task for students. This problem can serve as an introductory activity for a geometry class. This will facilitate their thinking in connecting geometry to algebra in order to come to a conclusion. In this particular case students will have to use the properties of squares to determine the dimensions of a rectangle, given the diagnol of a square. This activity will not only introduce these ideas to students, but it will introduce the necessary way of thinking in order to find success within a geometry class.
The Squares Problem
In the figure below, a rectangle has been cut into eleven squares of various sizes. The smallest square has a diagnol of 3*square root of 18. Determine the dimensions of the large rectangle.