In △ACD , B and E are two points on sides AC and AD respectively, such that BE is parellel to CD. CD = 9 cm, BE = 6 cm, AB = 5 cm and ED = 2 cm, Whatare the measures of the lengths ( in cm) of AE and BC ?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 4, 2.5
Given:
CD = 9 cm
BE = 6 cm
AB = 5 cm and
ED = 2 cm
Solution :
Since BE||CD
AB/AC = BE/CD = AE/AD
Now, AB/AC = 6/9
5/AC = 2/3
AC = 15/2
AC = AB + BC = 7.5
AC = 5 + BC = 7.5
BC = 2.5 CM
Also, AE/AD = 6/9
AE/(AE + ED) = 2/3
AE/(AE + 2) = 2/3
3AE = 2AE + 4
AE = 4.
Hence, measures of the lengths of AE and BC are 4 cm and 2.5 cm respectively.