Diagonals in the diamond

The length of one diagonal in diamond is 24 cm greater than the length of the second diagonal and diamond area is 50 m2. Determine the sizes of the diagonals.

Result

u1 =  1012.07 cm
u2 =  988.07 cm

Solution:

u2=u124 S=u1u22=u1(u124)2=50 m2=500000 cm2 2S=u1224u1 u224u1000000=0  a=1;b=24;c=1000000 D=b24ac=24241(1000000)=4000576 D>0  u1,2=b±D2a=24±40005762=24±8625092 u1,2=12±1000.0719974082 u1=1012.0719974082 u2=988.07199740819   Factored form of the equation:  (u1012.0719974082)(u+988.07199740819)=0 u>0 u1=1012.07  cm u_2 = u_1 - 24 \ \\ S = \dfrac{u_1 \cdot u_2}{2 } = \dfrac{u_1 \cdot (u_1-24)}{2 } = 50 \ m^2 = 500000 \ cm^2 \ \\ 2S = u_1^2-24 u_1 \ \\ u^2 -24u -1000000 =0 \ \\ \ \\ a=1; b=-24; c=-1000000 \ \\ D = b^2 - 4ac = 24^2 - 4\cdot 1 \cdot (-1000000) = 4000576 \ \\ D>0 \ \\ \ \\ u_{1,2} = \dfrac{ -b \pm \sqrt{ D } }{ 2a } = \dfrac{ 24 \pm \sqrt{ 4000576 } }{ 2 } = \dfrac{ 24 \pm 8 \sqrt{ 62509 } }{ 2 } \ \\ u_{1,2} = 12 \pm 1000.0719974082 \ \\ u_{1} = 1012.0719974082 \ \\ u_{2} = -988.07199740819 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ (u -1012.0719974082) (u +988.07199740819) = 0 \ \\ u>0 \ \\ u_1 = 1012.07 \ \text{ cm }
u2=u124=988.07  cm u_2 = u_1 - 24 = 988.07 \ \text{ cm }



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Math student
How comes about U1 and U2

#
Dr Math
u1, u2 = unknown diagonals.

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