Diamond

Side length of diamond is 35 cm and the length of the diagonal is 56 cm. Calculate the height and length of the second diagonal.

Result

v =  16.8 cm
u =  42 cm

Solution:

S1=S2 12av=12u1u2 1235v=1256u 35v=56u a2=(u1/2)2+(u2/2)2 352=(56/2)2+(u/2)2 v=14⋅56⋅u/(35)=16.8  cm  S_1 = S_2 \ \\ \dfrac12 a v = \dfrac12 u_1 u_2 \ \\ \dfrac12 35 v = \dfrac12 56 u \ \\ 35v = 56u \ \\ a^2 = (u_1/2)^2+(u_2/2)^2 \ \\ 35^2 = (56/2)^2+(u/2)^2 \ \\ v = \dfrac14 \cdot 56\cdot u / ( 35 ) = 16.8 \ \text{ cm } \ \\
u=4⋅ 352−562=42  cm u=\sqrt{ 4 \cdot \ 35^{ 2 }-56^{ 2 } } = 42 \ \text{ cm }

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Pythagorean theorem is the base for the right triangle calculator.
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