Magic Rectangle
Geometry
Level
2
Three squares are place side by side to form a rectangle. If the ratio of the length of the diagonal of the square to the length of the diagonal of a rectangle can be expressed in the form a/(√b) , where a and b are integers and a is square free, find a+b.
The answer is 6.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
Let the side of the square be 'x' cm. Then the Length of the rectangle=x+x+x=3x cm and the Breadth=x cm. Length of the diagonal of the square=√2* x and the Length of the diagonal of the rectangle= √10* x Ratio=√2* x/√10* x=√2/√10=1/√5. where a=1 and √(b )=√5 So, a+b=1+5=6 Simple.