Question

In ΔABC, DE || BC (as shown in the figure), If AD = 4 cm, AB = 9 cm and AC = 13.5 cm, then the length of EC is ______.

Options

• 6 cm

• 7.5 cm

• 9 cm

• 5.7 cm

Answer 1

In ΔABC, DE || BC (as shown in the figure), If AD = 4 cm, AB = 9 cm and AC = 13.5 cm, then the length of EC is 7.5 cm.

Explanation:

Given: AD = 4 cm, AB = 9 cm, and AC = 13.5 cm

Using the properties of similar triangles, when DE || BC, triangles ADE and ABC are similar.

From the similarity of the triangles: 

`(AD)/(AB) = (AE)/(AC)`

Now we can express AE in terms of AC, since AE + EC = AC:

`4/9 = (AE)/13.5`

AE = `4/9 xx 13.5`

AE = 6

Now EC will be:

EC = AC − AE

EC = 13.5 − 6

EC = 7.5