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Given: ABCD is a parallelogram m∠A = 60º ; BK ⊥ AD AK = KD; Perimeter of ABCD = 24 Find: BD.

Given: ABCD is a parallelogram m∠A = 60º ; BK ⊥ AD AK = KD; Perimeter of ABCD = 24 Find: BD.
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Given: ABCD is a parallelogram m∠A = 60º ; BK ⊥ AD AK = KD; Perimeter of ABCD = 24 Find: BD.

asked
User Collin Chaffin
by
7.3k points

1 Answer

3 votes
Since AK = KD, then the triangle ABD is isosceles,
Then BD = AB. Denote AB by x and AK by y.
Then,
2x+4y=24 (the perimeter)
cos 60=y/x.
From the second equation we get
y=0.5x
Plug in the first equation we get:

2x+4(0.5x)=24\\2x+2x=24\\4x=24\\x=6
We deduce that
BD=6.
answered
User Gretta
by
8.6k points
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