SOLUTION: an architect is allowed no more then 15 square meters to add a small bedroom to a house. Because of the rooms design in relationship to the existing structure, the width of it's re

Algebra ->  Rectangles -> SOLUTION: an architect is allowed no more then 15 square meters to add a small bedroom to a house. Because of the rooms design in relationship to the existing structure, the width of it's re      Log On


   

Question 390894: an architect is allowed no more then 15 square meters to add a small bedroom to a house. Because of the rooms design in relationship to the existing structure, the width of it's rectangle floor must be 7 meters less than two times the length. Find the precise length and width of the rectangular floor of maximum area that the architect is permitted.
~thanx
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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an architect is allowed no more then 15 square meters to add a small bedroom to a house.
Because of the rooms design in relationship to the existing structure, the width
of it's rectangle floor must be 7 meters less than two times the length.
Find the precise length and width of the rectangular floor of maximum area that the architect is permitted.
:
Let x = the required length
then
(2x-7) = the required width
:
The area:
x(2x-7) = 15
2x^2 - 7x - 15 = 0
You can solve this using the quadratic formula, but this will factor
(2x + 3)(x-5) = 0
The positive solution
x = 5 m is the length
then
2(5)-7 = 3 m is the width