Diagonals in the diamond

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

Correct answer:

u₁ =  1012.07 cm
u₂ =  988.07 cm

Step-by-step explanation:

$$\begin{gathered} u_2=u_1-24 \\ S=\frac{u_1\cdot u_2}{2}=\frac{u_1\cdot (u_1-24)}{2}=50m^2=500000c{m}^2 \\ 2S=u_1^2-24u_1 \\ {u}^2-24u-1000000=0 \\ a=1;b=-24;c=-1000000 \\ D=b^2-4ac=24^2-4\cdot 1\cdot (-1000000)=4000576 \\ D>0 \\ {u}_{1,2}=\frac{-b\pm \sqrt{D}}{2a}=\frac{24\pm \sqrt{4000576}}{2}=\frac{24\pm 8\sqrt{62509}}{2} \\ {u}_{1,2}=12\pm 1000.071997 \\ {u}_1=1012.071997408 \\ {u}_2=-988.071997408 \\ \text{ Factored form of the equation: } \\ (u-1012.071997408)(u+988.071997408)=0 \\ u>0 \\ {u}_1=1012.07\text{cm} \end{gathered}$$

$u_2=u_1-24=988.07\text{cm}$

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