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

Answer:

$DE=18.38$

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, $\frac{{\triangle}ADE}{ar ABC}=\frac{1}{2}$.

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

$\frac{ar ADE}{arABC}=\frac{1}{2}=\frac{(DE)^{2}}{(BC)^{2}}$

⇒$\frac{(DE)^{2}}{(BC)^{2}}=\frac{1}{2}$

⇒$\frac{(DE)^{2}}{(26)^{2}}=\frac{1}{2}$

⇒$(DE)^{2}=13{\times}26=338$

⇒$DE=18.38$