Question

in triangle abc angle b=90 , d and e are mid points of the sides ab and ac respectively. if ab=6 and ac=10, then find the length of de

Answer 1

$$\begin{gathered} \mathrm{AC}=10\mathrm{cm}\mathrm{and}\mathrm{AB}=6\mathrm{cm}, \\ \mathrm{In}△\mathrm{ABC}, \\ \mathrm{By}\mathrm{pythagoras}\mathrm{theorem}: \\ {\mathrm{AC}}^2={\mathrm{BC}}^2+{\mathrm{AB}}^2 \\ \Rightarrow \mathrm{BC}=\sqrt{100-36} \\ \Rightarrow \mathrm{BC}=8\mathrm{cm} \\ \mathrm{Since},△\mathrm{ADE}\mathrm{and}△\mathrm{ABC}\mathrm{are}\mathrm{similar}. \\ \mathrm{Therefore}, \\ \frac{\mathrm{DE}}{\mathrm{BC}}=\frac{1}{2} \\ \mathrm{Hence},\mathrm{DE}=4\mathrm{cm}. \end{gathered}$$