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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-> 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
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.
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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.
