A square is divided into five rectangles, and all the rectangles have the same area. Given that AB = 1, find the side length of the square.

Guest Aug 3, 2022

#3**+1 **

BuilderBoi already found the area to be 25/9

So the side of the square = sqrt (25/9) = 5/3

Here's the proof

The top of the square has the length 5/9 + 5/9 + 5/9 = 15/9 = 5/3

By symmetry the top edge of one of the two rectangles at the bottom = (5/3) (1/2) = 5/6

And the area of one of these rectangles = 5/9

So the other dimension of one of these rectangles must be (5/9) / (5/6) = 6/9 = 2/3

And AB = 1

So....the side of the square is also 1 + 2/3 = 5/3

CPhill Aug 3, 2022