# 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:

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

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Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Math student
How comes about U1 and U2

Dr Math
u1, u2 = unknown diagonals.

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