Question

Let D and E be points on sides AB and AC, respectively, of a triangle ABC, such that AD : BD = 2 : 1 and AE : CE = 2 : 3. If the area of the triangle ADE is 8 sq cm, then the area of the triangle ABC, in sq cm, is

Answer 1

Correct Answer: 30

Area of \(ΔADE=\frac{1}{2}\times AD\times AE\times sinA\)

\(=\frac{1}{2}\times 2x\times 2y\times SinA=8\)
\(⇒ xy SinA=4\)

The area of triangle ABC is now calculated as \(\frac{1}{2}\times AB\times A\times sinA\)

\(=\frac{1}{2}\times 3x\times 5y\times sinA\)

\(⇒\frac{15}{2}xy\space  sinA=\frac{15}{4}\times4=30\)
\(∴\) Area of \(ABC = 30\)