#### Question

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

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

\because 4 sides of the diamond are equal

\therefore the length of each side is \dfrac{16}{4} =4 cm

In the right triangle △BOC , ∠CBO = 30°

\therefore 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}

\therefore BD = 2BO = 4 \sqrt{3}