10 grade maths> ABCD is a trapezium in which AB II CD. If...

ABCD is a trapezium in which AB II CD. If angle ADC= twice angle ABC, AD = a cm and CD = b cm, then the length of AB is

VEDANT MATHUR , 7 Years ago

Grade 8

2 Answers

Ankit

Last Activity: 7 Years ago

We know that adjacent sides of trapezium are supplimentry therefore ADC + ABC= 180°. 3ABC = 180° therefore ABC =60° same way BAD=60° And ADC=120 ° sameway CBA = 120°. Draw a perpendicular DM bisecting AB Triangle ADM is formed with DAM =60°. cos60 = 1/2= AM/AD therefore AM/a=1/2 therefore AM=a/2. Same way the other side perpendicular CN should be drawn and by applying cos60 BN = a/2. The remaining part is same as `b` therefore AB = a/2 + a/2 + b = (a+b). Hope you got it

SR Roy

Last Activity: 7 Years ago

3ABC = 180° therefore ABC =60° Similarly BAD=60° And ADC=120 ° and CBA = 120° If we draw a perpendicular DM bisecting AB,Triangle ADM is formed with DAM =60°cos60 = 1/2= AM/AD therefore AM/a=1/2 or AM=a/2 Same way the other side perpendicular CN should be drawn and by applying cos60 BN = a/2The remaining part is same as `b` therefore AB = a/2 + a/2 + b = (a+b) Answer: The value of the length of AB is (a+b)cm. $\angle ADC + \angle ABC = 180^{\circ}$ We know that adjacent angles of trapezium are supplimentry.So