Notes
three equal area rectangles solution

Three Equal Area Rectangles

Solution by Pythagoras' Theorem

In the above diagram, consider the right-angled triangle $A B C$. Let $x$ be the length of $A D$, then $A B$ has length $x + 10$ and $C B$ has length $x - 10$. Let $y$ be the length of $A C$. Then applying Pythagoras' theorem to triangle $A B C$ yields:

As the rectangles have the same area, also $7 y = 10 x$ so $y = \frac{10}{7} x$. Putting this into the above equation,

which simplifies to $\frac{2}{49} x^2 = 200$, and this simplifies further to $x = 70$ and so $y = 100$. The area of the rectangles is therefore $700$.