Question

In a triangle $ABC$, a straight line parallel to $BC$ intersects $ABandAC$ at point $DandE$ respectively. If the area of $ADE$ is one-fifth of the area of $ABC$ and $BC=10cm$, then $DE$ equals

• A. $2cm$
• B. $2\sqrt{5}cm$
• C. $4cm$
• D. $4\sqrt{5}cm$

Answer 1

The correct option is B $2\sqrt{5}cm$

In similar triangles ADE and ABC, ${\left(\frac{DE}{BC}\right)}^2=\frac{areaof\Delta ADE}{areaof\Delta ABC}⟹(\frac{DE}{BC}{)}^2=\frac{1}{5}⟹(\frac{DE}{10})=\frac{1}{\sqrt{5}}⟹DE=\frac{10}{\sqrt{5}}=\frac{5\ast 2}{\sqrt{5}}⟹DE=2\sqrt{5}$