Question

If $\Delta ABC$ is an equilateral triangle and D, E and F are the midpoints of their respective sides, find the ratio of area of $\Delta ABC$ to that of $\Delta ADE+\Delta DBF+\Delta EFC.$

• A. 4
• B. 4/3
• C. 1/4
• D. 1/3
• E. 3/4

Answer 1

The correct option is B

4/3

Area of $\Delta$ADE= $\frac{1}{4}$Area of $\Delta$ABC

Area of $\Delta$ADE = Area of $\Delta$DBF = Area of $\Delta$EFC

Area of $\Delta$ADE + Area of $\Delta$DBF + Area of $\Delta$EFC

= $\frac{3}{4}$Area of $\Delta$ABC

$\Rightarrow \frac{Areaof\Delta ABC}{Areaof\Delta ADE+\Delta Areaof\Delta DBF+Areaof\Delta EFC}=\frac{4}{3}$