Question 1136807: A rectangular plot measures 12m by 5m. A path of constant width runs along one side and one end. If the total area of the plot and the path is 120m^2, find the width of the path.
Answer by ikleyn(52890)   (Show Source):
You can put this solution on YOUR website! .
The smaller rectangle has dimensions 12 by 5 meters with the difference of 12-5 = 7 meters.
Since the path has uniform width, the larger rectangle has dimensions that differ by 7 meters, too.
So, you need to find two numbers, whose product is 120 and whose difference is 7.
This task is 5 seconds for your mental work.
The answer is 15 and 8.
So, the larger rectangle has the length of 15 meters against 12 meters for smaller rectangle.
The difference of 3 meters = 15 - 12 is TWICE the width of the patn.
Hence, the answer is 3/2 = 1.5 meters.
ANSWER. The width of the path is 1.5 meters.
My congrats: you learned on how to solve such problem mentally !
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My other closely related lessons to it are the lessons
- Problems on the area and the dimensions of a rectangle surrounded by a strip
- Cynthia Besch wants to buy a rug for a room
- Problems on a circular pool and a walkway around it
in this site.
Also, you have this free of charge online textbook in ALGEBRA-I in this site
- ALGEBRA-I - YOUR ONLINE TEXTBOOK.
The referred lessons are the part of this online textbook under the topic
"Dimensions and the area of rectangles and circles and their elements".
Save the link to this online textbook together with its description
Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson
to your archive and use it when it is needed.
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