Question

In trapezium ABCD, AB∥DC. The sides AD and BC are produced to meet at E. AB = 15 cm, CD =

10 cm, AD = 4 cm and BC = 5 cm, then DE = ?​

Answer 1

hey there!!

In TRAPEZIUM ABCD AB||DC JOINING DA PRODUCED AND CB PRODUCED AT E WILL FORM A ∆ EDC

NOW IN ∆ EDC ,AB||DC

NOW AB||DC AND ED TRANSVERSAL SO ANGLE EAB=ANGLE EDC( CORRESPONDING ANGLES)

AND ANGLE E=ANGLE E( COMMON)

SO ∆EAB~∆EDC (BY AA CRITERION)

SO AB/DC=AE/DE

SOLVING IT NOW

AB/DE=1-AD/DE

HERE I AM TAKING AB AS 10cm and DC as 15 cm

putting the values of AB,DE AND AD

WE WILL GET DE AS 12 cm ( ans)