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Let A B Ca n dA B C ' be two non-congrue...

Let `A B Ca n dA B C '` be two non-congruent triangles with sides `A B=4,A C=A C^(prime)=2sqrt(2)` and angle `B=30^0` . The absolute value of the difference between the areas of these triangles is

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The correct Answer is:
4

`rArr cos 30^(@) = (a^(2) + 16 - 8)/(2 xx a xx 4)`
`(sqrt3)/(2) = (a^(2) + 8)/(8a)`
`rArr a^(2) - 4 sqrt3 a + 8 = 0`
`rArr a_(1) + a_(2) = 4 sqrt3, a_(1) a_(2) = 8`
`rArr |a_(1) -a_(2)| = 4`
`rArr |(1)/(2) a_(1) xx 4 sin 30^(@) - (1)/(2) a_(2) xx 4 sin 30^(@)| = 4 xx (1)/(2) xx 4 sin 30^(@)`
`rArr |Delta_(1) - Delta_(2)| = 4`
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