SOLUTION: The owners of the rectangular swimming pool in the illustration want to surround the pool with a crushed-stone border of uniform width. They have enough stone to cover 62 square me
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Question 1162373: The owners of the rectangular swimming pool in the illustration want to surround the pool with a crushed-stone border of uniform width. They have enough stone to cover 62 square meters. How wide should they make the border? (Hint: The area of the larger rectangle minus the area of the smaller is the area of the border. Assume a = 21 m and b = 8 m.)
https://www.webassign.net/tgintroalgp4/6-8-036-alt.gif
Word problems aren't my forte, but I'm trying to understand them better. Thanks again for your help. You don't necessarily have to give me the solution but if you substitute the numbers in the question and give me a different one I'll be able to understand and figure it out for future similar questions. Thanks! Found 2 solutions by solver91311, ikleyn:Answer by solver91311(24713) (Show Source):
The area of a rectangle is given by the length times the width. Since the length of the large rectangle, that is the pool and the walkway is the length, namely multiplied times the width, namely . Substituting the given values for and :
square meters.
The area of the walkway is the area of the large rectangle minus the area of just the pool, namely , so the area of the walkway is given by:
square meters
And we are given that this needs to be 62 square meters, so:
Solve the quadratic for the positive root to find the desired value of
John
My calculator said it, I believe it, that settles it
The area of the border is the difference of the area of the larger rectangle and the smaller rectangle.
The dimensions of the smaller rectangle are given: they are 21 meter and 8 meters.
If the uniform width of the border is w (as it is shown in your picture), then the dimensions
of the larger rectangle are 21+2w and 8+2w meters.
So the area of the larger rectangle is (21+2w)*(8+2w) square meters;
the area of the smaller rectangle is 21*8 square meters.
Having this, you can write the equation for the border area
(21+2w)*(8+2w) - 21*8 = 62 square meters.
At this point, the setup is completed.
You have the equation to find w.
This equation is quadratic relative the unknown w.
Reduce/simplify it to the standard form quadratic equation, and then solve it EITHER using the quadratic formula
OR by factoring, if it works.
I hope that from this point you will be able to complete the solution on your own.
If not - then let me know.
