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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.

 

 Aug 3, 2022
 #1
avatar+2446 
+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 \(5 \times {5 \over 9} = \color{brown}\boxed{25 \over 9}\)

 Aug 3, 2022
 #2
avatar+124596 
+1

Very nice, BuilderBoi !!!

 

 

cool cool cool

CPhill  Aug 3, 2022
edited by CPhill  Aug 3, 2022
edited by CPhill  Aug 3, 2022
 #3
avatar+113 
+2

Nice one, there, BuilderBoi...

 Aug 3, 2022
edited by tuffla2022  Aug 3, 2022
edited by tuffla2022  Aug 3, 2022
edited by tuffla2022  Aug 3, 2022

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