# Built-up area

John build up area 5 x 7 = 35 m2 with building with a wall thickness 30 cm. How many centimeters would have to subtract from thickness of the walls that built-up area fell by 9%?

Correct result:

x =  13.4 cm

#### Solution:

$a=5 \m \ \\ b=7 \m \ \\ (a-2x)(b-2x) = (1-9/100) ab \ \\ 4x^2 +x (-2a-2b)+ ab \cdot 9/100 = 0 \ \\ \ \\ 4x^2 -24x +3.15 =0 \ \\ \ \\ a=4; b=-24; c=3.15 \ \\ D = b^2 - 4ac = 24^2 - 4\cdot 4 \cdot 3.15 = 525.6 \ \\ D>0 \ \\ \ \\ x_{1,2} = \dfrac{ -b \pm \sqrt{ D } }{ 2a } = \dfrac{ 24 \pm \sqrt{ 525.6 } }{ 8 } \ \\ x_{1,2} = 3 \pm 2.8657459761814 \ \\ x_{1} = 5.8657459761814 \ \\ x_{2} = 0.13425402381858 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ 4 (x -5.8657459761814) (x -0.13425402381858) = 0 \ \\ \ \\ 0 < x < 30 \ cm \ \\ x = 13.4 \ \text{cm}$

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