+0

geometry

0
125
3

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
+2541
+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
+124697
+1

Very nice, BuilderBoi !!!

CPhill  Aug 3, 2022
edited by CPhill  Aug 3, 2022
edited by CPhill  Aug 3, 2022
#3
+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