Answer:
[tex]DE=18.38[/tex]
Step-by-step explanation:
It is given that the length of triangle base is 26 that is BC=26.
A line, which is parallel to the base divides the triangle into two equal area parts.
Therefore, from the given information, [tex]\frac{{\triangle}ADE}{ar ABC}=\frac{1}{2}[/tex].
Now, since it is given that A line, which is parallel to the base divides the triangle into two equal area parts, thus
[tex]\frac{ar ADE}{arABC}=\frac{1}{2}=\frac{(DE)^{2}}{(BC)^{2}}[/tex]
⇒[tex]\frac{(DE)^{2}}{(BC)^{2}}=\frac{1}{2}[/tex]
⇒[tex]\frac{(DE)^{2}}{(26)^{2}}=\frac{1}{2}[/tex]
⇒[tex](DE)^{2}=13{\times}26=338[/tex]
⇒[tex]DE=18.38[/tex]
