Rectangle

Calculate area of the rectangle if its length is 12 cm longer than its width and length is equal to the square of its width.

Result

S =  64 cm2

Solution:

a=12+b a=b2 b+12=b2  b2b12=0 b2b12=0  p=1;q=1;r=12 D=q24pr=1241(12)=49 D>0  b1,2=q±D2p=1±492 b1,2=1±72 b1,2=0.5±3.5 b1=4 b2=3   Factored form of the equation:  (b4)(b+3)=0 b=b1=4 a=b2=42=16 S=a b=16 4=64 cm2a=12 +b \ \\ a=b^2 \ \\ b+12=b^2 \ \\ \ \\ b^2-b-12=0 \ \\ b^2 -b -12=0 \ \\ \ \\ p=1; q=-1; r=-12 \ \\ D=q^2 - 4pr=1^2 - 4\cdot 1 \cdot (-12)=49 \ \\ D>0 \ \\ \ \\ b_{1,2}=\dfrac{ -q \pm \sqrt{ D } }{ 2p }=\dfrac{ 1 \pm \sqrt{ 49 } }{ 2 } \ \\ b_{1,2}=\dfrac{ 1 \pm 7 }{ 2 } \ \\ b_{1,2}=0.5 \pm 3.5 \ \\ b_{1}=4 \ \\ b_{2}=-3 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ (b -4) (b +3)=0 \ \\ b=b_{1}=4 \ \\ a=b^2=4^2=16 \ \\ S=a \cdot \ b=16 \cdot \ 4=64 \ \text{cm}^2

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