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

#1**+1 **

Let one of the sides of the rectangle containing AB be x.

The area of this rectangle is \(x \times 1 = x\)

There are 5 of these, so the area is \(5 \times x = 5x\)

But, note that because 3 rectangles share side AB, their width is also x, meaning 1 side of the square is \(3x\).

So, we have the equation \((3x)^2 = 5x\).

Solving, we find \(x = {5 \over 9}\), meaning the area is \(5 \times {5 \over 9} = \color{brown}\boxed{25 \over 9}\)

BuilderBoi Aug 3, 2022