Question 1171007: A farmer has a 40 ft by 100 ft rectangular field that he wants to reduce to 67.5% of its original size. How wide of a strip should he cut around the edge of his field to do this?
Answer by ikleyn(52781)   (Show Source):
You can put this solution on YOUR website! .
The reduced area (the area after reducing) is 40*100*0.675 = 2700 square feet.
Let x be the uniform width of the strip to cut it around the edge of the field.
Then the new dimensions are (100-2x) feet and (40-2x) feet, and the area equation is
(100-2x)*(40-2x) = 2700 square feet.
Now, the formal way is to reduce it to the standard form quadratic equation
and then solve it using the quadratic formula or factoring.
But you may notice that 2700 = 90*30,
so all you need is to subtract 10 from 100 and 40.
In other words, you mentally guess (with my help) that 2x = 10 feet; hence x= 5 feet is the solution and the answer.
Thus the problem is just solved and the answer is "the strip width is 5 feet".
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From my solution, learn two ways to solve the problem: formal algebraic solving via quadratic equation
and simple way solving it mentally.
To see many other similar solved problems, look into the lesson
- 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 lesson is 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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