SOLUTION: The length of a rectangle vegetable garden is 5 meters more than its width. Find the dimensions of the vegetable garden if its area is 204 square meters

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Question 1124076: The length of a rectangle vegetable garden is 5 meters more than its width. Find the dimensions of the vegetable garden if its area is 204 square meters
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Let x be the width; then the length is x+5. Then the area is length times width:

x%28x%2B5%29+=+204
x%5E2%2B5x-204+=+0
x%2B17%29%28x-12%29+=+0
x+=+-17 or x+=+12

Obviously -17 is not a valid width. So the width is 12m and the length is 17m.

To solve that problem algebraically, as above, we had to factor the x^2+5x-204 by finding two number whose product is 204 and whose difference is 5.

But that is exactly what the problem asks us to do... so the formal algebra doesn't help us any.

The easiest way to solve this problem is to forget the algebra and straight away look for two numbers whose product is 204 and whose difference is 5. A little trial and error finds the numbers 12 and 17.