## Problem Of The Week 27

**A golden rectangle is a rectangle in which the ratio of the width to length is the same as that of the length to the sum of the length and width. Which of the following is also true about a golden rectangle?
I. The ratio of the length to width is the same as the ratio of the width to the difference of the length and width.
II. The product of the length and width is equal to the product of the sum of the two sides and the difference of the two sides.
III. The length has to be greater than two times the width.**

**(1) Only I and II (2) Only II and III
(3) Only I and III (4) All the three statements**

(5) None of these(5) None of these

let width =w, length=l

Now, w/l=l/(w+l)

Taking inverse of this, l/w=(w+l)/l

Now, subtracting denominator from numerator from both the sides.(Pardon my ignorance.. but hve forgotten what is stands for componendo/dividendo stuff.. bachpan mein padha tha)

(l-w)/w=(w+l-l)/l

Taking inverse l/w=w/(l-w)

So I is true.

Now, again performing operations on this we get 2 as well

Now, for III, taking l=3, we get w as ~1.8

So, III isn’t true.

Answer option 1

P.S. implex please put the fundas of componendo/dividendo as to what is valid and what is not.

milindSeptember 25, 2008 at 4:59 pm

nicely done !

outtimedSeptember 25, 2008 at 10:21 pm