# Word Problem Issue

• Sep 18th 2012, 07:43 PM
marukai47
Word Problem Issue
I'm having serious problems solving this problem....

A golden rectangle is a rectagle whoes length is approximately 1.6 times the width. The early Greeks thought that a rectangle with these dimensions was the most pleasing to the eye and examples of the golden rectangle are found in many early works of art. For exampls, the Parthenon in Athens contains many examples of golden rectangles. Mike Hallaham would like to plant a rectangle garden in the shape of a golden rectagnle. If he has 78 feet of fencing available, find the dimensions of the garden.

what is the width of the garden and the length?
• Sep 18th 2012, 08:17 PM
DIOGYK
Re: Word Problem Issue
Let l be the length of the fence and w be the width. you know that lenth is approximately 1.6 times width, so you have your first equation: $l=1.6w$. Since there's 78 feet of fence available, and fence is a rectangle, which means that it has 4 sides (2 length and 2 width), $2l+2w=78$, now you have your second equation which means you'll be able to solve for both variables by method of substitution or addition and after solving it for l and w, you will have the dimensions of the fence.
• Sep 18th 2012, 08:26 PM
marukai47
Re: Word Problem Issue
when trying to solve I got w=−(1-39) and l=1 which is wrong
• Sep 18th 2012, 08:33 PM
DIOGYK
Re: Word Problem Issue
Quote:

Originally Posted by marukai47
when trying to solve I got w=−(1-39) and l=1 which is wrong

How did you get that results?

$l=1.6w$, substitute that in the second equation $2l+2w=78$ and you will get $2(1.6w)+2w=78$ -> $3.2w+2w=78$ -> $5.2w=78$ -> $w=\frac{78}{5.2}$ -> $w=15$. Since $l=1.6w$, $l=1.6*15=24$.