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A concrete mixer needs to know how wide to make a walk around a rectangular fountain that is 10 by 15 feet.
She has enough concrete to cover 200 sq. ft. To the nearest tenth of a foot, how wide should the walk be in order to use up all the concrete?
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Let x be the uniform width of the concrete walk.
The outer dimensions of the concrete walk are (10+2x) and (15+2x) feet.
The area equation is
(10+2x)*(15+2x) - 10*15 = 200.
Simplify and reduce to the standard quadratic equation
4x^2 + 50x - 200 = 0,
or
2x^2 + 25x - 100 = 0.
It is not factorable, so apply the quadratic formula.
= = .
Take the positive root
x = = 3.2 (rounded).
ANSWER. The uniform width of the concrete walk is 3.2 feet.
Solved.
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My other closely related lessons to it are
- 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.