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Length of the diagonal of a quadrilateral...?
In the quadrilateral ABCD, diagonal AC and BD cut at E. If AB=DA, BC=CD, AE=10, CE=20 and angle ABC = angle CDA = angle AED = 90 degree, find BD.
2 Answers
- 7 years agoFavorite Answer
draw ur diagram its like a kite;
since angle adc and abc are 90 degree
BD cut angle ADC asssume
adb = x, bdc = 90-x
now tan x=10/DE
tan 90-x = 20/DE
cot x = 20/DE
DE = 20/cot x
substitute in above so
tan square x = 1/2
tan x = 1/sqrt 2
....tan x= 1/sqrt 2 = 10/DE
there fore DE= 10_/2
and BD is 20sqrt 2
that is 28.284 units
