Question

Let AB // ED , AB = 10 units, AC = 12 units, and DE = 5 units. What is the length of AD?​

Answer 1

length of CD = 18 units.

Explanation:

In ΔABC and ΔCED,

AB║DE and AD is a transversal line,

m∠ABC = m∠CED [Alternate interior angles]

m∠ACB = m∠DCE [Vertically opposite angles]

ΔABC ~ ΔCED [By AA property of similarity]

Therefore, by the property of similar triangles, corresponding sides will be proportional.

`(AB)/(DE)= (AC)/(DC)`

`(10)/(5)=(12)/(CD)`

CD = 6

Since, AD = AC + CD

AD = 12 + 6

= 18 units

Therefore, length of CD = 18 units.