Squares!

Geometry Level 2

$C$ and $D$ are the centers of the orange square and the green square. $M$ is the midpoint of $CD$ . $MN \perp AB$ . Calculate $\frac{AB}{MN}$

This is part of the series: " It's easy, believe me! "

1 solution

Marta Reece
Aug 17, 2017

If $a$ is the distance from the center of smaller square to the edge, and $b$ is the same for the larger square then:

Distance $AB=2a+2b=2(a+b)$ .

Distance $MN=m=$ average of $a$ and $b$ $=\dfrac{a+b}2$

Therefore $\dfrac{AB}{MN}=\dfrac{2(a+b)}{\frac{a+b}2}=\boxed4$

nice solution,

azadali jivani - 3 years, 9 months ago

Great problem

Mike Davison - 3 years, 7 months ago