# Diamond

Calculate the length of the two diagonals of the diamond if:

a = 13 cm
v = 12 cm

Correct result:

u1 =  21.63 cm
u2 =  14.42 cm

#### Solution:

$a = 13\ cm \ \\ h = 12 \ cm \ \\ \ \\ q^2 = a^2 -h^2 \ \\ q = \sqrt{a^2 -h^2} = 5 \ cm \ \\ \ \\ u_1^2 = h^2 + (a+q)^2 \ \\ u_1 = \sqrt{ h^2 + (a+q)^2} = 21.63 \ \text{cm} \ \\$
$u_2^2 = h^2 + (a-q)^2 \ \\ u_2 = \sqrt{ h^2 + (a-q)^2} = 14.42 \ \text{cm} \ \\$

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