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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
Solution
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
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