SOLUTION: a rectangular building is 25m long and 15m wide. a path of constant width is laid around the whole building. if the area of the path is 90m2.calculate the with of the path to the n

Question 164691: a rectangular building is 25m long and 15m wide. a path of constant width is laid around the whole building. if the area of the path is 90m2.calculate the with of the path to the nearest mm.
Answer by checkley77(12844) (Show Source): You can put this solution on YOUR website!
25*15=375 m^2 is the building area.
(25+2x)(15+2x)=375+90
375+50x+30x+4x^2=465
4x^2+80x+375-465=0
4x^2+80x-90=0

x=(-80+-sqrt[80^2-4*4*-90])/2*4
x=(-80+-sqrt[6400+1440])/8
x=(-80+-sqrt[7840]/8
x=(-80+-88.544)/8
x=(-80+88.544)/8
x=8.544/8
x=1.07 m. is the width of the path.
Proof:
(25+2*1.07)(15+2*1.07)=375+90
(25+2.14)(15+2.14)=465
27.14*17.14=465
465~465

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