# 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:

$S_1 = S_2 \ \\ \dfrac12 a v = \dfrac12 u_1 u_2 \ \\ \dfrac12 35 v = \dfrac12 56 u \ \\ 35v = 56u \ \\ a^2 = (u_1/2)^2+(u_2/2)^2 \ \\ 35^2 = (56/2)^2+(u/2)^2 \ \\ v = \dfrac14 \cdot 56\cdot u / ( 35 ) = 16.8 \ \text { cm } \ \\$
$u=\sqrt{ 4 \cdot \ 35^{ 2 }-56^{ 2 } } = 42 \ \text { cm }$

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#### Following knowledge from mathematics are needed to solve this word math problem:

Pythagorean theorem is the base for the right triangle calculator. See also our trigonometric triangle calculator.

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