Question

15. Find the length of segment DE of the triangle ABC.

Answer 1

Answer:

Option C. $26\ units$

Step-by-step explanation:

we know that

Triangles ADE and ABC are similar by AA similarity postulate

AB=2AD

Apply proportion

$\frac{AD}{AB}=\frac{8x-6}{12x+4}\\ \\\frac{AD}{2AD}=\frac{8x-6}{12x+4}\\ \\\frac{1}{2}=\frac{8x-6}{12x+4}\\ \\12x+4=16x-12\\ \\16x-12x=4+12\\ \\4x=16\\ \\x=4\ units$

Find the length of segment DE

$DE=8x-6=8(4)-6=26\ units$