SOLUTION: a floor plan for a new house includes a rectangular dining room that measures by 5m by 4m. the owners want a larger dining room with an area of 25m^2. the architect re-designs the

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Question 1181936: a floor plan for a new house includes a rectangular dining room that measures by 5m by 4m. the owners want a larger dining room with an area of 25m^2. the architect re-designs the floor plan by adding a strip of floor of uniform width to the two adjacent sides of the dining room. how wide should the strip be to the nearest tenth of a meter? write a therefore sentence.
Found 2 solutions by Boreal, ikleyn:
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
the new dimensions will be 5+2x by 4+2x, where x is the width in meters of the strip. Each side will be 2x longer
That product 20+18x+4x^2=25
so 4x^2+18x-5=0
x=(1/8)(-18+/- sqrt (324+80)): sqrt 404=20.10
use only the positive root
the width is 2.10/8 m or 0.2625 m (26.25 cm)
this rounds to 0.3 m width, which is the answer
the dimensions are 5.6 x 4.6m=25.76 m^2

Answer by ikleyn(52750)   (Show Source): You can put this solution on YOUR website!
.


            Tutor @Boreal misread the problem, so his solution is not adequate.

            I came to bring a correct solution. 


After adding the strip of the wide  "x"  to two adjacent sides, the new dimensions of the room 


will be (4+x) and (5+x), so the area equation is


    (4+x)*(5+x) = 25  square meters.


Simplify, reduce to a quadratic equation, write it in the standard form and use the quadratic formula to find the roots


    20 + 4x + 5x + x^2 = 25

    x^2 + 9x - 5 = 0

     =  = .


You need only positive root,  so  the value


     = 0.525... = 0.5 (rounded)  will be your approximate ANSWER.

Solved, answered and carefully explained.


////////////


At the end of your post,  I see an instruction which requires to write  "a therefore sentence",
but I always consider such instructions as  idiotic.


Avoid place them to your posts.



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