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QUESTION: A garden is divided into 4 parts by 2 walkways that go through the center parallel to sides.  Determine width of walkways.

Dimensions of garden - 50 by 40 ft.

Total area of walkways - 261 sq. ft.

Thanks.

ANSWER: Suppose the walkways are w feet wide.
area of walkways = 50w + (40-w)w = 261
w² - 90w + 261 = 0
4w² - 180w + 261 = 0

w = [90 ± √(90² – 4·1·261)] / [2·1]
= [90 ± √7056] / 2
= [90 ± 84] /2
= 3, 87
87 is an extraneous solution
w = 3

The walkway is 3 feet wide.

---------- FOLLOW-UP ----------

QUESTION: "w² - 90w + 261 = 0
4w² - 180w + 261 = 0"

I don't understand these steps.  Thanks again.

ANSWER: Please ignore the "4w² - 180w + 261 = 0". It was supposed to be deleted but I missed it. Sorry for the confusion.

---------- FOLLOW-UP ----------

QUESTION: 'w² - 90w + 261 = 0"

I don't understand this step.  Thanks.

Randy
The blue walkway is 50w ft².
The purple walkway is (40-w)w ft².
Total area of walkways is 261 ft².

50w + (40-w)w = 261
50w + (40w - w²) = 261
90w - w² = 261
w² - 90w + 261 = 0

By the quadratic formula, w = 3, 87,
The walkway must be narrower than 40 ft, so 87 is an extraneous solution.
The walkway is 3 feet wide.
Questioner's Rating
 Rating(1-10) Knowledgeability = 10 Clarity of Response = 10 Politeness = 10 Comment "ANSWER: Please ignore the "4w² - 180w + 261 = 0". It was supposed to be deleted but I missed it. Sorry for the confusion." No problem. Fast, courteous, friendly, helpful response !!

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#### Janet Yang

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