Question 1162373
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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 *[tex \Large a\,+\,2w] multiplied times the width, namely *[tex \Large b\,+\,2w].  Substituting the given values for *[tex \Large a] and *[tex \Large b]:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ (21\,+\,2w)(8\,+\,2w)\ =\ 4w^2\ +\ 58w\ +\ 168] square meters.


The area of the walkway is the area of the large rectangle minus the area of just the pool, namely *[tex \Large a\cdot b\ =\ 168], so the area of the walkway is given by:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 4w^2\ +\ 58w] square meters


And we are given that this needs to be 62 square meters, so:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 4w^2\ +\ 58w\ =\ 62]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 4w^2\ +\ 58w\ -\ 62\ =\ 0]


Solve the quadratic for the positive root to find the desired value of *[tex \Large w]
								
								
John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
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*[tex \Large \ \
*[tex \LARGE \ \ \ \ \ \ \ \ \ \  
								
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