In △ABC, D and E are the points on sides AC and BC, respectively such that DE || AB. F is a point on CE such that DF || AE. If CE = 6 cm, and CF = 2.5 cm, then BC is equal to:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e 14.4 cm
Given;
DE || AB & DF || AE & CE = 6 cm and CF = 2.5 cm
As we can see that in △CDF and in △CAE,
CD/CA = CF/CE (Similar triangle property)
So,
CD/CA = 2.5/6 .................. (1)
Now, In △CDE and △CAB,
CD/CA = CE/CB (Similar triangle property)
From equation 1:
2.5/6 = 6/BC .................. (2)
⇒ BC = (6 × 6) / 2.5
⇒ BC = 14.4 cm