Question

A triangle is formed by joining the coordinates B(0,0), C(8,0) and A(4,8). DE is joined where D is the mid-point of AB, and E is the mid-point of AC. DC and BE is joined to intersect at F.
Then, Area of triangle DFB = (x) $\times$ Area of triangle EFC, where x is an integer. The value of x is

• A. 3
• B. 2
• C. 1
• D. 0.5

Answer 1

The correct option is C 1

Since, D is the mid-point of AB, and E is the mid-point of AC in triangle ABC. From mid-point theorem, line joining the mid points of two sides is parallel to third side and is equal to half of it.

DC$\parallel$BC

Since, triangles between the same base and same parallels have equal area.
Thus, Area of $\Delta$ DCB = Area of $\Delta$ BEC.

$\Rightarrow$ Area of $\Delta$ DCB- Area of $\Delta$ BFC = Area of $\Delta$ BEC- Area of $\Delta$ BFC

$\Rightarrow$ Area of $\Delta$ DFB = Area of $\Delta$ EFC

$\Rightarrow$ Area of $\Delta$ DFB = (1)$\times$Area of $\Delta$ EFC

Hence, value of x = 1