2016 · Q83
ABC is a triangle in which D is the midpoint of BC and E is the midpoint of AD. Which of the following statements is/are correct?
- 1The area of triangle ABC is equal to four times the area of triangle BED.
- 2The area of triangle ADC is twice the area of triangle BED.
Select the correct answer using the code given below.
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A1 only
- B2 only
- CBoth 1 and 2
- DNeither 1 nor 2
Explanation
D bisects BC, so area(ABD) = area(ADC) = Δ/2. E bisects AD, so area(BED) = area(ABD)/2 = Δ/4. Thus area(ABC) = 4·area(BED) and area(ADC) = 2·area(BED). Both statements are true, option C.