geometry

[sud21]

The perimeter of the rhombus ABCD is 42. If measurement of angle ADC is 60, what is the length of BD?

[shankar.ashwin]

We could use this using basic trigonometry, but then it would not be a valid GMAT problem..

Extend DC and drop a perpendicular from B to meet DC at (say) O

Now BOC is a 30-60-90 triangle with hyp = BC

Since its a rhombus, all sides are equal. Hence BC = 42/4 = 10.5

Since side opposite 90 is 10.5, side opposite to 30 would be 10.5/2 = 5.25
and side opposite 60 would be = 5.25 Sqrt(3) (perpendicular)

Now DO = DC+CO = 10.5+5.25 = 15.75 and perpendicular (BO) = 5.25 Sqrt(3)

We can find BD using pythagoras theorem.