Question

PLEASE, I NEED HELP FOR A CLASS. The length of triangle base is 26. A line, which is parallel to the base divides the triangle into two equal area parts. Find the length of the segment between triangle legs

Answer 1

`DE=18.38`

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,
`\frac{{\triangle}ADE}{ar ABC}=(1)/(2)`.

Now, since it is given that A line, which is parallel to the base divides the triangle into two equal area parts, thus

`(ar ADE)/(arABC)=(1)/(2)=((DE)^(2))/((BC)^(2))`

⇒
`((DE)^(2))/((BC)^(2))=(1)/(2)`

⇒
`((DE)^(2))/((26)^(2))=(1)/(2)`

⇒
`(DE)^(2)=13{*}26=338`

⇒
`DE=18.38`