In ΔABC, points E and F are on sides AB and AC respectively such that 4AE = 3AB and 4AF = 3AC. If BC = 20 cm, then what is the length of EF (in cm)?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 15
If a line cuts two sides of a triangle in the same ratio, it is parallel to the third side (converse of the basic proportionality theorem), and the small triangle it cuts off is similar to the whole triangle.
On side AB, \(4AE=3AB\) gives \(\displaystyle \frac{AE}{AB}=\frac{3}{4}\)
On side AC, \(4AF=3AC\) gives \(\displaystyle \frac{AF}{AC}=\frac{3}{4}\)
Both sides are cut in the same ratio, so EF is parallel to BC and \(\triangle AEF\sim\triangle ABC\)
Corresponding sides are in the same ratio: \(\displaystyle \frac{EF}{BC}=\frac{3}{4}\), so \(\displaystyle EF=\frac{3}{4}\times20=15\) cm
