The perimeter of diamond $$ ABCD $$ is 16 cm,
$$ ∠ABC＝60° $$ , the diagonal lines $$ AC $$ and $$ BD $$ intersects at point $$ O $$ .
Find the length of $$ AC $$ and $$ BD $$

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Uniteasy Admin · Accepted Answer

$$ \because $$ 4 sides of the diamond are equal
$$ 	herefore $$ the length of each side is $$ \dfrac{16}{4} =4 $$ cm
In the right triangle $$ △BOC $$ , $$ ∠CBO = 30° $$
$$ 	herefore OC = \dfrac{1}{2} BC = 2 $$ , $$ AC = 4 $$
According to The Pythagorean Theorem,
$$ BO^2 = BC^2-OC^2 $$
$$ BO = \sqrt{4^2-2^2} =2\sqrt{3}  $$
$$ 	herefore BD = 2BO = 4 \sqrt{3} $$

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