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Alexxx [7]
3 years ago
11

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

Mathematics
1 answer:
AveGali [126]3 years ago
3 0
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.
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Step-by-step explanation:

In this particular case we have the following system of equations:

y

=

−

3

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+

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[

E

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1

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+

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=

−

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[

E

q

.

2

]

Substituting

[

E

q

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1

]

in

[

E

q

.

2

]

:

x

+

4

(

−

3

x

+

4

)

=

−

6

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−

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x

=

−

22

−

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=

2

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E

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.

1

]

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