SOLUTION: One formula stating the relationship between the length l and width of a rectangle of “pleasing proportion”is w L^2 = w(L + w). How should a 4 foot by 8 foot sheet of plasterbo

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Question 1207822: One formula stating the relationship between the length l and width of a rectangle of “pleasing proportion”is w L^2 = w(L + w). How should a 4 foot by 8 foot sheet of plasterboard be cut so that the result is a rectangle of “pleasing proportion” with a width of 4 feet?
Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
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One formula stating the relationship between the length highlight%28cross%28l%29%29 L and width w of a rectangle
of “pleasing proportion” is highlight%28cross%28w%29%29 L^2 = w(L + w). How should a 4 highlight%28cross%28foot%29%29 feet by 8 highlight%28cross%28foot%29%29 feet sheet
of plasterboard be cut so that the result is a rectangle of “pleasing proportion” with a width of 4 feet?
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Let's take w= 4 feet and find L from this equation

    L^2 = w*(L + w).


So,  

    L^2 = 4*(L + 4)

    L^2 - 4L - 16 = 0

    L%5B1%2C2%5D = %284+%2B-+sqrt%284%5E2+-+4%2A%28-16%29%29%29%2F2 = %284+%2B-+sqrt%2880%29%29%2F2 = 2+%2B-+2%2Asqrt%285%29.


We disregard the negative root and accept the positive one  L = 2%2B2%2Asqrt%285%29 = 6.472135955.


So, the cut should be at L = 6.472 feet from the 4 ft edge.    ANSWER

Solved.

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By the way, this problem was solved at this forum many years ago (~ 15 years ago) under this link
https://www.algebra.com/algebra/homework/quadratic/Quadratic_Equations.faq.question.669064.html