# 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.

Correct result:

u1 =  1012.07 cm
u2 =  988.07 cm

#### Solution:

$u_2 = u_1 - 24 \ \\ S = \dfrac{u_1 \cdot u_2}{2 } = \dfrac{u_1 \cdot (u_1-24)}{2 } = 50 \ m^2 = 500000 \ cm^2 \ \\ 2S = u_1^2-24 u_1 \ \\ u^2 -24u -1000000 =0 \ \\ \ \\ a=1; b=-24; c=-1000000 \ \\ D = b^2 - 4ac = 24^2 - 4\cdot 1 \cdot (-1000000) = 4000576 \ \\ D>0 \ \\ \ \\ u_{1,2} = \dfrac{ -b \pm \sqrt{ D } }{ 2a } = \dfrac{ 24 \pm \sqrt{ 4000576 } }{ 2 } = \dfrac{ 24 \pm 8 \sqrt{ 62509 } }{ 2 } \ \\ u_{1,2} = 12 \pm 1000.0719974082 \ \\ u_{1} = 1012.0719974082 \ \\ u_{2} = -988.07199740819 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ (u -1012.0719974082) (u +988.07199740819) = 0 \ \\ \ \\ u>0 \ \\ u_1 = 1012.07 \ \text{cm}$
$u_2 = u_1 - 24 = 988.07 \ \text{cm}$

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Math student
How comes about U1 and U2

Dr Math
u1, u2 = unknown diagonals.

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