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 Question from Mark, a parent: Please Help. I'm trying to help my Child and I have no clue on this math question. Rectangular shapes with a length to width ratio of approximately 5 to 3 are pleasing to the eye. The ratio is know as the golden ratio. A designer can us the expression 1/3(5w) to find the length of such a rectangle with width 6 inches.

Hi Mark,

We have two responses for you

I am not surprised that you are baffled by this question. It is an extremely confusing way to ask a very natural question. How about this?

Rectangular shapes with a length to width ratio of approximately 5 to 3 are pleasing to the eye.
The ratio is know as the golden ratio. A designer wishes to construct a rectangle with width 6 inches and with the ratio of its length to its width the golden ratio. What should its length be?

To me this is a much more natural way to ask the question. I would answer something like this.

A rectangle with length 5 inches and width 3 inches satisfies the Golden Ratio and the designer wants one that is twice the width so he needs its length to be twice the length of 5 inches, that is $2 \times 5 = 10 \mbox{ inches.}$

If he wanted one of width 12 inches then, since $12 = 3 \times 4$ he would need a length of $5 \times 4 = 20$ inches. Similarly if he wanted one of width 1 inch, then since 1 is one-third of 3 he would need a length of one-third of 5 inches or $\frac13 \times 5 = \frac13 (5) = \frac53$ inches. This is how the textbook author comes up with the algebraic expression "1/3(5w)." Here w stands for the width the designer wants and then the length is 1/3(5w), or I would prefer to express it $\frac53 w.$

Penny

The question is not phrased as a question! This is a bad habit of some math text writers.

The implied question is: if the width w = 6 inches, find 1/3(5w). Does this help?

Good Hunting!
RD

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