One fifth of the area of the triangle ABC is cut off by the line
| One fifth of the area of the triangle ABC is cut off by the line DE drawn parallel to BC such that D is on AB and E is one AC. If BC = 10 cm, then what is DE equal to?
A. √5 cm
B. 2√5 cm
C. 3√5 cm
D. 4√5 cm
Please scroll down to see the correct answer and solution guide.
Right Answer is: B
SOLUTION
In triangle ADE and ABC
∠ A is common
∠ ADE = ∠ ABE [∵ Corresponding angles are equal when DE is parallel to BC]
∴ ADE ∼ ABC
Area(ADE) /Area(ABC) = (DE/BC)2
⇒ 1/5 = (DE/10)2
∴ DE = 2√5 cm
